Answer:
Step-by-step explanation:
Answer: 6
there are 24 fish and 4 tanks so divide 24 by 4 and you'll have 6
Answer:
the number of fish in each tank is 6
Step-by-step explanation:
becuause 24 divided be 4 is 6
Clay has $50 on his bus pass and it’s $3.00 each time he rides. He will be able to ride the bus twice a day for 11 days? True or false?
Given that each bus ride is $3, and that assuming the takes the ride twice a day,
[tex]\begin{gathered} \text{Amount spent a day on bus ride = 2 }\times\text{ \$3} \\ =\text{ \$6} \end{gathered}[/tex]If he takes the ride in the same manner for 11 days,
[tex]\begin{gathered} \text{Amount spent in 11 days = 11 }\times\text{ \$6} \\ =\text{ \$ 66} \end{gathered}[/tex]Thus, he needs $66 to ride the bus twice for 11 days.
Since Clay has $50, he will not be able to ride the bus twice for 11 days.
Hence, the correct answer is False
To insure a house valued at £3000 costs £2.25. Find the value of a house which costs £3.37 1/2 to insure.
Using the cross-multiplication method, we know that the house which costs £3.37 has a value of £4,493.33.
What is a cross-multiply method?One might cross-multiply an equation between two fractions or rational expressions in mathematics, more specifically in elementary arithmetic and elementary algebra, to make the equation simpler or to find the value of a variable.When using the cross-multiplication approach, the denominator of the first term is multiplied by the numerator of the second term and vice versa.So, the value of the house costs £3.37:
House that costs £2.25 is valued at £3000.Now, use the cross-multiplication method as follows:
2.25/3000 = 3.37/x2.25x = 3000 × 3.372.25x = 10,110x = 10,110/2.25x = 4,493.33Therefore, using the cross-multiplication method, we know that the house which costs £3.37 has a value of £4,493.33.
Know more about a cross-multiply method here:
https://brainly.com/question/28839233
#SPJ1
Correct question:
To ensure a house valued at £3000 costs £2.25. Find the value of a house that costs £3.37.
There are 1.5 litres of water in a bottle.
There are 250 millilitres of water in another bottle.
Work out the total amount of water in the two bottles
Answer:
1.75 liters
Step-by-step explanation:
250 mililters is a quarter of 1 litre
Show that(x+1)(x+3)(x+5)can be written in the form ax^3+bx^2+cx+d where a,b,c and d are all positive integers.
The given expression : (x + 1)(x + 3)(x + 5) can be written as (x³ + 9x² + 23x + 15)
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following expression -
(x + 1)(x + 3)(x + 5)
We have -
(x + 1)(x + 3)(x + 5)
x{(x + 3)(x + 5)} + 1{(x + 3)(x + 5)}
x(x + 3)(x + 5) + (x + 3)(x + 5)
(x² + 3x)(x + 5) + (x + 3)(x + 5)
x²(x + 5) + 3x(x + 5) + x(x + 5) + 3(x + 5)
x³ + 5x² + 3x² + 15x + x² + 5x + 3x + 15
x³ + 9x² + 23x + 15
which is same of the form
ax³ + bx² + cx + d
Therefore, the given expression : (x + 1)(x + 3)(x + 5) can be written as (x³ + 9x² + 23x + 15)
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
brainly.com/question/14441381
#SPJ1
ANSWER MY QUESTIONS PLEASE .........? A paddleboat can move at a speed of 14 kilometers per hour in still water. The boat is paddled 10 kilometers downstream in a river in the same time it takes to go 5 kilometers upstream. What is the speed of the river? Round your answer to the nearest tenth. AND A woman drives an SUV that gets 13 miles per gallon (mpg). Her husband drives a hybrid that gets 60 mpg. Every week, they travel the same number of miles. They want to improve their combined mpg. They have two options on how they can improve it.
Option 1: They can tune the SUV and increase its mileage by 1 mpg and keep the hybrid as it is.
Option 2: They can buy a new hybrid that gets 85 mpg and keep the SUV as it is.
Compute and state the combined mpg for each option. Round your answers to the nearest tenth. Then tell which option will give a better combined mpg.
Answer:
Step-by-step explanation:
the suv question the first option would make the suv go from 13 mpg to 14 mpg and add 14 to 60 to get 74 and divided by 2 to get 37 is their average mpg
Options two would make the hybrid 85 mpg and the suv still 13 add them together to get 98 and divide them by 2 to get 49
Option 2 will give more mileage
paddle boat question
10/14+x=5/14-x
Cross multiply
10(14-x)=5(14+x)
140-10x=70+5x
70=15x
70/15=x
X=4.7 is the speed of the current
Please don’t quote me on this paddle boat one XD
Hopes this helps
help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
The length of shorter feet is 2.5 ft and the length of longer feet is 6.5 ft.
By Pythagorean theorem,
[tex]( Hypotenuse)^{2} = (Base)^{2}+ (Perpendicular)^{2}[/tex]
Let base = x
perpendicular = x+4
Hypotenuse = 7
Putting the value in equation,
[tex]7^{2} = x^{2} +(x+4)^{2}[/tex]
[tex]49 = x^{2} +x^{2}+8x+16[/tex]
[tex]2x^{2} +8x+16-49=0[/tex]
[tex]2x^{2} +8x-33=0[/tex]
[tex]x = \frac{-8 + \sqrt{64 - 4(2)(-33)} }{2*2}[/tex] or [tex]\frac{-8 - \sqrt{64 - 4(2)(-33)} }{2*2}[/tex]
[tex]x=\frac{-8 + \sqrt{64 +264} }{4}[/tex] or [tex]\frac{-8 - \sqrt{64 +264} }{4}[/tex]
[tex]x = \frac{-8 + \sqrt{384} }{4}[/tex] or [tex]\frac{-8 - \sqrt{384} }{4}[/tex]
[tex]x = \frac{-8+18.1}{4}[/tex] or [tex]\frac{-8-18.1}{4}[/tex]
[tex]x = \frac{10.1}{4}[/tex] or [tex]\frac{-26.1}{4}[/tex]
[tex]x = 2.5[/tex] or [tex]-6.5[/tex]
As, length can't be negative, we will take x = 2.5
Therefore, x+ 4 = 2.5 + 4
= 6.5
Hence, the length of shorter feet is 2.5 ft and the length of longer feet is 6.5 ft.
Learn more about length on:
https://brainly.com/question/8552546
#SPJ1
solve 6/7 dividid 36/56 and put the answer in simplest form. A. 6/8 B. 8/6 C. 4/3 2/8
The correct answer is C. (4/3)
Fraction calculation steps:
6/7 ÷ 36/56 = 6/7 × 56/36 = (6×56)/(7×36) = 336/252
(336÷84)/(252÷84) = 4/3
Learn more about fraction here: brainly.com/question/78672
#SPJ1
Let ZD be an acute angle such that cos D = 0.64. Use a calculator to approximate the measure of ZD to the nearest tenthof a degree.m/D
Given:
[tex]\cos D=0.64[/tex]D is an acute angle
Find-:
The value of D
Explanation-:
The angle D is:
[tex]\begin{gathered} \cos D=0.64 \\ \\ D=\cos^{-1}(0.64) \\ \\ D=50.208 \end{gathered}[/tex]The value of the nearest tenth is 50.2
5. 2. A rectangular print is 36 inches long and 24 inches wide. It will be placed inside a rectangular frame that is 2 inches wide on all sides. What is the area when the print is inside the frame A. 864 in. B. 960 in? C. 980 in. D. 1,120 in.
Since the frame has 2 inches wide on all sides, the frame measures:
Then, the area of the frame is
[tex]\begin{gathered} A=\text{basexheight} \\ A=40\times28 \end{gathered}[/tex]which gives
[tex]A=1120in^2[/tex]then, the answer is 1120 inches squared, which corresponds to option D.
i need help figuring out how to know which one goes where
Simplify each of the expressions
[tex]undefined[/tex]When using an equivalent fraction to find a percent why do you write 100 as the denominator?
We do so beacuse it is easy to convert a fraction to a percent when the denominator is 100.
What is equivalent fraction?Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value.
What is denominator?Denominator is the part of a fraction that is below the line and that functions as the divisor of the numerator.
What is percentage?A percentage or percent is a fraction that always has the denominator as 100.
When using an equivalent fraction to find a percent we write 100 as denominator.
If a fraction does not have a denominator of 100, you can convert it to an equivalent fraction with a denominator of 100, and then write the equivalent fraction as a percent.
We do so because it is easy to convert a fraction to a percent when the denominator is 100.
To know more about equivalent fractions, visit
https://brainly.com/question/1797146
#SPJ1
Light intensity (I) is proportional (a) to the inverse square of distance (d) of a subject from a lightsource. The relationship in intensities for subjects at different distances from the same source canbe likewise seen as a ratio or proportional relationship.I x 1 1A proportional relationship can be mathematically expressed as follows for light intensity (I) inlumens when a subject is at the light source.=Lumens at origin or sourceSo, if a light intensity (I) is 569 lumens at the source, what is the light intensity (I) at 9 distancefrom the source,?Round the value to the nearest tenth if necessary. You do not need to include a label for lumens.Only the number, rounded to the tenth, will be necessary.
ANSWER
The light intensity is 7.0
STEP-BY-STEP EXPLANATION:
What to find? The value of the proportionality constant.
Given parameters
• Light intensity = 569 lumens
,• Distance = 9
According to the question, Light intensity (I) is proportional to the inverse square of the distance.
This can be expressed mathematically as
Let the intensity of light be represented as I
Let the distance be represented as d
[tex]I\text{ }\propto\text{ }\frac{1}{d^2}[/tex]The next thing is to introduce a constant k
[tex]\begin{gathered} I\text{ = }\frac{K\cdot\text{ 1}}{d^2} \\ I\text{ = }\frac{K}{d^2} \end{gathered}[/tex]Recall that,
I = 569 lumens
d = 9
The next thing is to substitute the parameters into the above formula
[tex]\begin{gathered} \frac{Lumens\text{ at current distance}}{\text{Lumens at origin or source}}\text{ = }\frac{1}{d^2} \\ \frac{\text{Lumens at current distance}}{\text{5}69}\text{ = }\frac{1}{(9)^2} \\ \frac{\text{Lumens at current distance}}{\text{5}69}\text{ = }\frac{1}{81} \\ \text{Cross multiply} \\ 569\cdot\text{ }1\text{ = Lumens at current distance }\cdot\text{ 81} \\ \text{Divide both sides by 81} \\ \frac{569}{81}\text{ = }\frac{Lumens\text{ at current distance }\cdot\text{ 81}}{81} \\ \text{Lumens at current distance = 7.0} \end{gathered}[/tex]Only quadratic functions can be transformed. true or false
It is false, that only quadratic functions can be transformed.
Given that,
To justify the statement, "Only quadratic functions can be transformed."
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
It is not necessary that only quadratic functions can be transformed, all the functions can be transformed regardless of their nature such as linear functions, polynomial functions etc.
Thus, It is false, that only quadratic functions can be transformed.
learn more about function here:
brainly.com/question/21145944
#SPJ1
Reflect the given coordinate points across the line y= x
Given the points:
[tex]\begin{gathered} B\colon(-3,-1) \\ C\colon(-3,3) \\ D\colon(0,3) \end{gathered}[/tex]We need to reflect the points over the line y = x
The rule of reflection is as follows:
[tex](x,y)\rightarrow(y,x)[/tex]So, the points after reflection will be:
[tex]\begin{gathered} B^{\prime}\colon(-1,-3) \\ C^{\prime}\colon(3,-3) \\ D^{\prime}\colon(3,0) \end{gathered}[/tex]What happens if the rate of change is not constant in a function?
Answer:
time will be a straight line, and you can find the rate of change by calculating the slope of the line. If the rate of change is not constant, a graph of the measured quantity vs. time will be curved instead of straight
Step-by-step explanation:
Answer:
When the rate of change is constant, the graph results in a straight line. When the rate of change is not constant, the graph will include a curved line.
Step-by-step explanation:
1. A cylindrical jar has a radius of 6 inches and a height of 10inches. The jar is filled with marbles that have a
volume of 20 in³. Use 3.14 for pi. Show work. Complete sentences.
a. What is the volume of the jar?
V= πr ² h
Using the formula of volume of cylinder, the volume of the jar is 1130.4 cube inches.
In the given question we have to find the volume of the jar.
From the question,
A cylindrical jar has a radius of 6 inches
So r=6 inches
A cylindrical jar has a height of 10 inches
So h=10 inches
The jar is filled with marbles that have a volume of 20 cube inches.
As we know that the volume of cylinder is
V=πr^2h
where V= volume of cylinder
r = radius
h= height
π=3.14
Putting the value
V=3.14*(6)^2*10
V=3.14*36*10
V=1130.4 cube inches
To learn more about volume of cylinder link is here
brainly.com/question/16134180
#SPJ1
Clare has $102.38 in her savings account. At the ATM, she deposits 3 checks she received for her birthday. Each check was written for $15.00. Then, she withdraws $20 in cash. What is Clare's new account balance?
Answer:
127.38
Step-by-step explanation:
Answer:
127.38
Step-by-step explanation:
15 x 3 = 45
(102.38 + 45) - 20 = 127.38
Shannon invests money in a bank account which gathers
compound interest each year.
After 5 years there is $673.40 in the account.
After 8 years there is $737.99 in the account.
Work out the annual interest rate of the bank account.
Give your answer as a percentage to 1 d.p.
By using the concept of compound interest, rate of interest is 3.1 %
What is compound interest?
If the interest on a certain principal at a certain rate over a certain time increase exponentially rather than linearly, the interest earned is called Compound interest.
If the principal is P, rate is r and time is t, then amount is
[tex]A = P(1 + \frac{r}{100})^n[/tex]
Let the principal be $P and the rate be r% per annum
After 5 years there is $673.40 in the account.
[tex]673.40 = P(1 + \frac{r}{100})^5\\[/tex]............. (1)
After 8 years there is $737.99 in the account.
[tex]737.99 = P(1 + \frac{r}{100})^8[/tex] ................. (2)
Dividing (2) by (1),
[tex](1 +\frac{r}{100})^3 = 1.096\\\\1 + \frac{r}{100} = (1.096)^{\frac{1}{3}}\\\\1 + \frac{r}{100} = 1.031\\\\\frac{r}{100} = 1.031 -1\\\\\frac{r}{100} =0.031\\\\r = 0.031 \times 100\\[/tex]
r = 3.1 %
Rate is 3.1 %
To learn more about compound interest, refer to the link-
https://brainly.com/question/24274034
#SPJ13
SOMEONE PLSS HELP FOR QUESTION 1
Answer:
triangle abc is has same degres of angles with triangle def, but def is smaller in 3 times. it's only what i know, sorry if i not help
i think yea, they has a same angles, but def smaller in 3 times so i think yes
help meeeeeeeeee pleasee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
Measurement and conversion (d = rt) Mackenzies bike can go 12 mph. She needs to be at a store at 10:00 A.M.. Of the store is 20 miles away, what time will she need to leave?
We have to use the equation
[tex]d=rt[/tex]Where r = 12 mph, d = 20 miles, let's find t.
[tex]\begin{gathered} 20=12t \\ t=\frac{20}{12}=\frac{10}{6}=\frac{5}{3} \end{gathered}[/tex]She'll take 5/3 hours to get there which is equivalent to 1 2/3 hours.
Let's transform 2/3 hours to minutes to find the exact time she has to leave.
We know that 1 hour is 60 minutes.
[tex]\frac{2}{3}hr\cdot\frac{60\min}{1hr}=\frac{120}{3}\min =40\min [/tex]So, she will take exactly 1 hour and 40 minutes.
If you have to get there at 10:00 A.M., then she has to leave at 8:20 A.M.If Jalen had 109 inches of string and Kelly had 3 yards of string, who had more string?
Answer: Jalen has more string then Kelly
Step-by-step explanation:
Converting Kelly's string from yards, to inches to match up with Kelly's length of string we use the formula:
#yd = (# × 36) = total amount of "
Inputting the information in the formula, It'd look like this:
5 yd = (5 × 36) = 108"
therefore, from this information the answer to the question, is Jalen.
In 1991, minimum wage was $4.25 per hour; in 1997, minimum wage increased in $5.15 per hour. Find the rate of change in the minimum wage per year from 1991 to 1997.
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{x}{year}&\stackrel{y}{wage}\\ \cline{1-2} 1991&4.25\\ 1997&5.15\\ \cline{1-2} \end{array} \hspace{5em} (\stackrel{x_1}{1991}~,~\stackrel{y_1}{4.25})\qquad (\stackrel{x_2}{1997}~,~\stackrel{y_2}{5.15}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5.15}-\stackrel{y1}{4.25}}}{\underset{run} {\underset{x_2}{1997}-\underset{x_1}{1991}}} \implies \cfrac{0.90}{6}\implies \cfrac{0.15}{1}\implies 0.15~\frac{\$}{year}[/tex]
Connor was given a box of assorted chocolates for his birthday. Each night, Connortreated himself to some chocolates. There were originally 18 chocolates in the boxand after 3 nights, there were 9 chocolates remaining in the box. Write an equationfor C, in terms of t, representing the number of chocolates remaining in the box tdays after Connor's birthday.
The equation for C in terms of t is C = 18 – 3t.
Algebra is the area of mathematics that aids in expressing issues or circumstances into mathematical expressions.
Given that Connor was given a box of assorted chocolates for his birthday
The box originally contained 18 chocolates.
There were still 9 chocolates in the box after three nights.
Now we have to find the equation for C in terms of t
18 – 9 = 9
After 3 nights
9 / 3 = 3
18 = chocolates at the beginning.
C = 18 – 3t
Therefore the equation for C in terms of t is C = 18 – 3t.
To learn more about algebra visit
https://brainly.com/question/21196212
#SPJ9
The graphs of 3x + 9y = 15 and y = mx - 4
are parallel lines. What is the value of m?
The graph of equations [3x + 9y = 15] and [y = mx - 4] are not parallel and the value of m is 13/3.
What are graphs?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.Although 'graph' and 'chart' are sometimes used interchangeably, they are two separate types of images. Charts are tables, graphs, or images that concisely and clearly organize enormous volumes of data. Charts are used by people to forecast the future and evaluate existing facts. However, graphs emphasize the basic data and display changes over time.So, the graph of the equations:
3x + 9y = 15y = mx - 4The value of m:
y = mx - 4: Equation is in the form of the slope.Now,
y = mx - 49 = 3m - 4Now, solve for m as follows:
9 = 3m - 43m = 9+43m = 13m = 13/3Now, plot the graph as follows:
(Refer to the graph attached below)It is clearly visible that the lines of both equations are not parallel.
Therefore, the graph of equations [3x + 9y = 15] and [y = mx - 4] are not parallel and the value of m is 13/3.
Know more about graphs here:
https://brainly.com/question/28953186
#SPJ1
Which statement best explains whether y = 2x -3 is a linear function or a nonlinear function
y= 2x-3 is a linear function because the graph contains the points (0, −3), (1, −1), (2, 1), which are on a straight line.
Which statement best explains whether y = 2x − 3 is a linear function or a nonlinear function?
it is a linear function because the graph contains the points (0, −3), (1, −1), (2, 1), which are on a straight line.
It is a nonlinear function because the graph contains the points (0, −3), (1, −1), (2, 1), which are not on a straight line.
It is a linear function because the graph contains the points (−3, 0), (−1, 1), (1, 2), which are on a straight line.
It is a nonlinear function because the graph contains the points (−3, 0), (−1, 1), (1, 2), which are not on a straight line.
A linear equation has the following form:
y = mx + b
where
m is the slope
b is the y-intercept.
Given:
y = 2x - 3
by comparing it with linear equation,
y = y
m = 2
x = x
b = -3
so by this we can conclude that
y = 2x -3 is a linear function because the graph contains the points (0, −3), (1, −1), (2, 1), which are on a straight line
You can also perform a vertical line test. If the line touches your graphed function in more than one spot, it is not a function.
If you want to know about non-linear function, click on this link
https://brainly.com/question/22574744
Part A:
Solve this equation 1/2x-7=1/3(x-12)
Part B:
Explain or show your reasoning.
x = 18 in the equation given in the question that is 1/2x-7=1/3(x-12).
Simple equations is a linear equation involving variables with degree one. It contains mainly one variable.
Part A -
⇒ 1/2x-7=1/3(x-12)
⇒ 1/2x-7 = x/3 - 4
⇒ x/2 - x/3 = -4 + 7
⇒ 3x - 2x/6 = 3
⇒ x/6 = 3
⇒ x = 18
Part B -
According to equation 1/2x-7=1/3(x-12) we need to find x . So, first we open the brackets on the right hand side and then bring the variables to the l.h.s and the constants to the r.h.s . After that we take the lcm of x/2 and x/3 and equate it to 3. Then we get the value of x as 18.
Hence, x = 18 in the equation 1/2x-7=1/3(x-12).
To understand more about Simple equations refer -
https://brainly.com/question/18831322
#SPJ1
The graph of f(x) = 2x is shown on the grid. (First attachment)
The graph of g(x) = (One-half)x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)? (The rest of the attachments are the options)
The graph that represents the function g(x) = (1/2)^x is given as follows:
The last graph.
How to obtain the rule for function g(x)?The parent function f(x) has the definition presented as follows:
f(x) = 2^x.
The transformation that the function f(x) undergoes is defined as follows:
Reflection over the y-axis.
The rule that defines a function g(x) after a reflection of f(x) over the y-axis is given as follows:
g(x) = f(-x).
Hence the function g(x) is defined as follows:
g(x) = f(-x) = 2^(-x) = (1/2)^x.
As the negative exponent means that the base is inverted.
Then the graph of the exponential function has these following features:
Decreasing, as the base has an absolute value less than 1.Crosses the y-axis at y = 1, as when x = 0, y = (1/2)^0 = 1.Hence the last graph is the correct option.
More can be learned about reflections at https://brainly.com/question/28980122
#SPJ1
Compare: 4.3 x 10^6 O 12 x 10^5A.>B.
To check the bigger or smaller number, we can adjust the numbers such that they both have the same exponential power.
The first number can be written as shown below:
[tex]4.3\times10^6=4.3\times10\times10^5=43\times10^5[/tex]Now, both numbers have the same exponent. Therefore, we can compare the numbers 43 and 12.1.
Observation of the numbers on the number line shows that:
[tex]43>12.1[/tex]Therefore, we have that:
[tex]43\times10^5>12.1\times10^5[/tex]The correct option is OPTION A.
The population of a city is P(t) = 4e^0.03t(in millions), where t is measured in years.(a) Calculate the doubling time of the population.(b) How long does it take for the population to triple in size?(c) How long does it take for the population to quadruple in size?
a) Doubling time of the population.
Initial population = 4
Doubling = 2 x 4 = 8
[tex]8=4e^{0.03t}[/tex]Then, solve for t:
[tex]\begin{gathered} \frac{8}{4}=\frac{4e^{0.03t}}{4} \\ 2=e^{0.03t} \end{gathered}[/tex]Apply the exponent laws:
[tex]\begin{gathered} \ln 2=0.03t \\ \frac{\ln2}{0.03}=\frac{0.03t}{0.03} \\ t=23.1\approx23 \end{gathered}[/tex]Answer a: 23 years
b) Initial population = 4
Triple the population = 3 x 4 = 12
Therefore:
[tex]\begin{gathered} 12=4e^{0.03t} \\ \frac{12}{4}=\frac{4e^{0.03t}}{4} \\ 3=e^{0.03t} \\ \ln 3=0.03t \\ \frac{\ln 3}{0.03}=\frac{0.03t}{0.03} \\ t=36.6\approx37 \end{gathered}[/tex]Answer b: 37 years
c) Initial population = 4
Quadruple the population = 4 x 4 = 16
So:
[tex]\begin{gathered} 16=4e^{0.03t} \\ \frac{16}{4}=\frac{4e^{0.03t}}{4} \\ 4=e^{0.03t} \\ \ln 4=0.03t \\ \frac{\ln 4}{0.03}=\frac{0.03t}{0.03} \\ t=46.2\approx46 \end{gathered}[/tex]Answer c: 46 years