The population of a town in Texas is modeled by the function f(x)=16,007(1.031)x. If the initial population (that is, the population when x=0) was measured January 1, 2014, what will the population be on January 1, 2030? Round your answer to the nearest whole number, if necessary.
Answers
From the information available, the initial population was 16,007. That figure was taken as at the year zero which is January 1, 2014.
This means
[tex]\begin{gathered} Yr1=2015-2014 \\ Yr2=2016-2014 \\ Yr3=2017-2014 \end{gathered}[/tex]This trend would be used until we get to January 1, 2030, when we would calculate as follows;
[tex]Yr16=2030-2014[/tex]Note that the years count from Jan 1 to Jan 1.
The function that models the yearly growth is;
[tex]f(x)=16007(1.031)^x[/tex]Using the first year, 2014 which is year zero, the result would remain 16,007. That is;
[tex]\begin{gathered} f(0)=16007(1.031)^0 \\ f(0)=16007\times1 \end{gathered}[/tex]For the 16th year, which is year 2030, we woud now have the following;
[tex]\begin{gathered} f(16)=16007(1.031)^{16} \\ f(16)=16007(1.629816253511204) \\ f(16)=26,088.4687699\ldots \end{gathered}[/tex]Rounded to the nearest whole number, this figure becomes;
ANSWER:
[tex]\text{Population}\approx26,088[/tex]Related Questions
Geometry Translation Please help me. This is worth alot of point.
Answers
In a proof what is the reason that justifies this statement:
Segment BP is congruent to segment BP.
Answers
Answer: I believe that the BP segment is equal to BP segment because of the reflexive property.
Step-by-step explanation:
The required reason is that segment BP is congruent to segment BP that Segment BP is the common side among both triangles.
In congruent geometry, the shapes that are so identical. can be superimposed on themselves.
Here,
The necessary explanation is that segment BP and segment BP are congruent because segment BP is the common side of both triangles BPS and BPY, as shown in the figure.
Thus, the required reason is that segment BP is congruent to segment BP and that Segment BP is the common side among both triangles.
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a. A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 45 months and a standard deviation of 3 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 48 and 51 months?b. The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 64 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 57 and 64?c. A population of values has a normal distribution with μ=153 and σ= 39.5You intend to draw a random sample of size n=196Find P2, which is the score separating the bottom 2% scores from the top 98% scores. P2 (for single values) = Find P2, which is the mean separating the bottom 2% means from the top 98% means. P2 (for sample means) = Enter your answers as numbers accurate to 1 decimal place. round your answer to ONE digit after the decimal point! Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.d. A population of values has a normal distribution with μ= 117.8 and σ=73.1You intend to draw a random sample of size n=59Find the probability that a single randomly selected value is greater than 113. P(X > 113) = Find the probability that a sample of size n= 59 is randomly selected with a mean greater than 113. P(M > 113) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Answers
a.
For this to make sense, we will plot the bell curve of the distribution.
It is general convention that:
65% of the values in the distribution lie between
[tex]\begin{gathered} \bar{x}\pm\sigma \\ Where\colon \\ \bar{x}=\text{mean} \\ \sigma=s\tan dard\text{ deviation} \end{gathered}[/tex][tex]\begin{gathered} 48\pm3=51\text{ or 45} \\ \text{This means that }65\text{ \% of the values lie within the range 45 and 51.} \\ Therefore,\text{ the range between 48 and 51 will be a half of 65\%} \\ \frac{65}{2}\text{ \% = 32.5\%} \end{gathered}[/tex]35% is the percentage of cars that remain in service between 48 and 51 months
b.
We also plot the distribution curve as in a above,
[tex]\begin{gathered} 64\pm7=71\text{ or }57 \\ \text{This means that }65\text{ \% of the values lie within the range 57 and 71.} \\ Therefore,\text{ the range between 57 and 64 will be a half of 65\%} \\ \frac{65}{2}\text{ \% = 32.5\%} \end{gathered}[/tex]
32.5% is the approximate percentage of lightbulb replacement requests numbering between 57 and 64
A popular resort hotel has 300 rooms and is usually fully booked. About 7% of the time a reservation is canceled before the 6:00 p. M. Deadline with no penalty. What is the probability that at least 285 rooms will be occupied? use the binomial distribution to find the exact value.
Answers
The probability that at least 285 rooms will be occupied is 0.0885
A popular resort hotel's reservation follows Normal distribution as size of sample is greater than 30 with mean np and standard deviation √npq
Given , Probability of cancelation : q = 7% = 0.07
Probability of no cancellation of room : p = 1 - q
p = 1 - 0.07
p = 0.93
here, Binomial distribution tends to normal
Sample size : n = 300
Mean = np
= 300 × 0.93
= 279
Standard deviation = [tex]\sqrt{npq}[/tex]
= [tex]\sqrt{(300)(0.93)(0.07)}[/tex]
= [tex]\sqrt{19.53}[/tex]
= 4.42
We have to find P(x ≥ 285)
subtracting 279 and dividing by 4.42 to each sides
P(x ≥ 285) = [tex]P(\frac{x - 278}{4.42} \geq \frac{285 - 278}{4.42} )[/tex]
= P(z ≥ 1.357) = 1 - P(z<1.357)
Using Z probability table ,
P(x ≥ 285) = 1 - (0.9115)
= 0.0885 is required probability
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The measure of an angle is 74° what is the measure of its complementary angle
Answers
Answer:
16 degrees
Step-by-step explanation:
Complementary angles = 90 degrees
If the measure of one angle is 74 degrees, that means that the measure of the other angle that is complementary to it is 16 degrees.
74 + x = 90
x = 16
Jones, JacobTranslation T maps the point (1, 3) to (2,6). Which of the following rules describes the translation T?OT: (x, y) (2., 2y)OT: (0,y) – (a, fu)OT:(,y) - (x-1,7 - 3)OT:(,) ( + 1, y + 3)
Answers
The given points are (1,3) and (2,6).
The pre-image is (1,3) and the image is (2,6).
As you can observe, the image is double than the pre-image, this means the transformation used was a dilation with a scale factor of 2, the rule is
[tex]OT\colon(x,y)\rightarrow(2x,2y)[/tex]Therefore, the right answer is the first choice.V ABCD - EFGH. What is the value of k? Your answer may be exact or rounded to the nearest tenth. Note: Images are not to scale. A E 4 mm k 8 mm B 6 mm H D 6 mm F 8 mm 4 mm C С
Answers
Since rectangles ABCD and EFGH are similar, we can take the ratios of the corresponding sides of the rectangles
[tex]\frac{AB}{AD}=\frac{EH}{EF}[/tex][tex]\frac{8}{4}=\frac{k}{6}[/tex]cross multiplying
8 x 6 = 4 x k
48 = 4k
4k = 48
Divide both sides by 4
k = 48/4
k = 12
IS THE ANSWER 1, 3, 17, 57 or none of the aboveIf none of the above please write the correct answer!Please answer step by step explanation
Answers
ANSWER
None of the above.
EXPLANATION
We want to solve the equation given for x:
[tex]\sqrt[]{x-1+5}=9[/tex]First, simplify the radical:
[tex]\sqrt[]{x+4}=9[/tex]Now, find the square of both sides of the equation:
[tex]\begin{gathered} (\sqrt[]{x+4})^2=9^2 \\ x+4=81 \end{gathered}[/tex]Finally, simplify by subtracting 4 from both sides of the equation:
[tex]\begin{gathered} x=81-4 \\ x=77 \end{gathered}[/tex]Hence, the correct option is "None of the above".
Use the diagram to the right to determine whether BC. DE. Justify your answer. AD = 15, DB = 12, AE = 10, and EC = 8. The cut part is BC (top to bottom)
Answers
Explanation:
AD = 15, DB = 12, AE = 10, and EC = 8
To determine if line BC is parallel to line DE, we will find the ratio of thier corresponding sides. if it is equal, they are parallelf
A rectangular prism has a width of 4 cm, a height of 3 cm and a depth of 5 cm. What is the volume of the prism?
Answers
We have that the equation of the volume of a rectangular prism is:
[tex]V=w\cdot h\cdot d[/tex]in this case, we have the following information:
[tex]\begin{gathered} w=4\operatorname{cm} \\ h=3\operatorname{cm} \\ d=5\operatorname{cm} \end{gathered}[/tex]then, using the formula we have:
[tex]\begin{gathered} V=4\cdot3\cdot5=12\cdot5=60 \\ V=60\operatorname{cm}^3 \end{gathered}[/tex]therefore, the volume of the prism is 60 cm^3
The number of murders and robberies per 100,000 population for a random selection of states is shown.
Answers
The equation of the regression line has the following shape:
[tex]y=mx+b[/tex]Where m is calculated through the following equation:
[tex]m=\frac{N\sum^{}_{}xy-\sum^{}_{}x\sum^{}_{}y}{N\sum^{}_{}x^2-(\sum^{}_{}x)^2}[/tex]And b is calculated through the following equation:
[tex]b=\frac{\sum^{}_{}y-m\sum^{}_{}x}{N}[/tex]N is the number of samples. 8 for this case.
The values of all the sums present in the above equation are reported in the last row of the table:
[tex]\begin{gathered} \sum ^{}_{}x=31 \\ \sum ^{}_{}y=680.1 \\ \sum ^{}_{}xy=3202.71 \\ \sum ^{}_{}x^2=142.52 \\ \sum ^{}_{}y^2=80033.99 \end{gathered}[/tex]Now, we can begin calculating m by replacing the values:
[tex]\begin{gathered} m=\frac{8\cdot3202.71-31\cdot680.1}{8\cdot142.52-31^2} \\ m=25.333 \end{gathered}[/tex]The slope of the equation is m = 25.333.
Now, we can calculate b:
[tex]\begin{gathered} b=\frac{680.1-25.333\cdot31}{8} \\ b=-13.153 \end{gathered}[/tex]Now that we know the parameters m and b for the linear regression, we can build the equation:
[tex]\begin{gathered} y=mx+b \\ y=25.333x-13.153 \end{gathered}[/tex]Where x represents the murders and y the robberies per 100,000 population.
Then, (a): the equation of the regression line is y = 25.333x - 13.153.
To predict the robberies per 100,000 population when x = 4.5 murders, we just need to replace that 4.5 in the equation that we just found:
[tex]y=25.333\cdot4.5-13.153=100,85[/tex]Finally, (b): according to the linear regression, the number of robberies per 100,000 population when x = 4.5 murders is approximately 100,85.
Please help me 2/3+ (-1/3)
Answers
Answer:
The answer is 1/3.
Step-by-step explanation:
The plus sign before the parenthesis means that everything inside keeps it's signal. So
[tex]\frac{2}{3}+(-\frac{1}{3})=\frac{2}{3}-\frac{1}{3}=\frac{2-1}{3}=\frac{1}{3}[/tex]The answer is 1/3.
Amir drove from Jerusalém to the lowest place on the earth Dead Sea. His latitude to sea level as a function of time is graphed.What was amir altitude at the beginning of the drive?
Answers
Answer:
440 meters.
Explanation:
At the beginning of the drive, time (on the x-axis) is 0.
The value of y when x=0 is 440 meters.
Therefore, Amir's altitude at the beginning of the drive is 440 meters.
The price for five pounds of
candy is $8. How much does it cost for
one pound?
Answers
Answer:
1.60
8/5=1.60
Step-by-step explanation:
Answer: $1.60
Step-by-step explanation: Easy, just divide 8 by 5. 8/5 = 1.6
(-20x)( 3xy-y/x^2 )( 3x/9x^2-3x )
Answers
When we simplify the given expression, the given expression equals to -20(3x-y)/x(3x-1)
Expression is a combination of variables, numbers and symbols (operations) which is defined according to some rules. We can apply any formula or solve the given expression according to the operations provided.
Given expression
-20x(3x-y/x^2)(3x/9x^2-3x)
Multiply each term with another term
= -20x × (3x-y)/x^2 × 3x/9x^2-3x
In first term and second term cancel x from numerator and denominators and from last expression take 3x common
= -20 × (3x-y)/x × 3x/3x(3x-1)
Cancel 3x from numerator and denominator in last term and we will get the final result.
= -20 × (3x-y)/x × 1/(3x-1)
= -20(3x-y)/x(3x-1)
The given question is incomplete, the complete question is
Simplify the following expression
(-20x)( 3xy-y/x^2 )( 3x/9x^2-3x )
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make a tree diagram to show the sample space. then, give the total number of outcomes. question 1. making a meal with chicken or steak and broccoli, carrots, potatoes,or green beans.
Answers
The sample space which is the total possibilities is 4
Use the long division method to find the result when 6x4 +423-7x²+3x-7 is
divided by 2x2 + 2x-3. If there is a remainder, express the result in the form
q(x) +5(2).
Answers
Answer:−6x4−3x3−2x2−4x−7x2+3=−6x2−3x+16+5x−55x2+3.
Step-by-step explanation: −6x4−3x3−2x2−4x−7x2+3. The Long Division method: −6x2−3x+16
In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The meanresponse was 5.2 with a standard deviation of 2.4.(a) What response represents the 95th percentile?(b) What response represents the 60th percentile?(c) What response represents the first quartile?...
Answers
Solution
[tex]\begin{gathered} \text{Given} \\ \operatorname{mean},\text{ }\mu=5.2 \\ \text{standard deviation, }\sigma=2.4 \\ \\ \text{Recall the formula} \\ Z=\frac{x-\mu}{\sigma} \\ x-\mu=Z\sigma \\ x=Z\sigma+\mu \end{gathered}[/tex](a)
[tex]\begin{gathered} Z-\text{score for 95 percentile = 1.645} \\ x=Z\sigma+\mu \\ x=1.645(2.4)+5.2 \\ x=9.148 \\ x=9.15\text{ (2 decimal places)} \end{gathered}[/tex](b)
[tex]\begin{gathered} Z-\text{score for 60 percentile = }0.253 \\ x=Z\sigma+\mu \\ x=0.253(2.4)+5.2 \\ x=5.8072 \\ x=5.81\text{ (2 decimal places)} \end{gathered}[/tex](c)
[tex]\begin{gathered} Z-\text{score for first quartile (25\%) = }-0.674 \\ x=Z\sigma+\mu \\ x=-0.674(2.4)+5.2 \\ x=3.5824 \\ x=3.58\text{ (2 decimal places)} \end{gathered}[/tex]Harper learned to play a total of 4 pieces over the course of 2 weeks of piano lessons. After 4 weeks of piano lessons, how many total pieces will Harper be able to play? Assume the relationship is directly proportional.
Answers
Step-by-step explanation:
Harper learned to play a total of 4 pieces over the course of 2 weeks of piano lessons. After 4 weeks of piano lessons, how many total pieces will Harper be able to play? Assume the relationship is directly proportional.
4 pieces / 2 weeks = 2 pieces per week
after 4 weeks:
4 weeks * 2 pieces per week = 8 pieces after 4 weeks
Answer:
8 pieces will be learnt in 4 weeks
Step-by-step explanation:
please mark as brainliestWrite an equation in slope-intercept form for the line with a slope of -1 and a y-intercept of -2.
Answers
Answer:
y = -x - 2
Step-by-step explanation:
Write an equation in slope-intercept form for the line with a slope of -1 and a y-intercept of -2.
slope-intercept form: y = mx + b where m = slope and b = y-intercept
when:
slope of -1
y-intercept of -2
then:
y = -1x + (-2)
y = -x - 2
Answer:
y= -x-2
Step-by-step explanation:
y=mx+b
slope=m
y intercept=b
m= -1
b= -2
input values of m and b to get equation:
y=(-1)x+(-2)
y= -1x-2
y = -x-2
y= -x-2
pls mark as brainliest
x/0.6= 9/0.5 Solve for x please
Answers
The solution of the equation given as x/0.6= 9/0.5 is x= 10.8
How to determine the solution of the equation?The equation is given as
x/0.6= 9/0.5
There are no constants to add or subtract in the equation
So, we have
x/0.6= 9/0.5
Multiply through the equation by 0.6
This gives
0.6 * x/0.6= 9/0.5 * 0.6
Evaluate the products
0.6 * x/0.6= 10.8
Evaluate the products, again
x= 10.8
Hence, the solution is 10.8
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WILL GIV BRAINLIEST Fred spent $3.15 on 4 1/2 pounds of peanuts. How much did he pay for each pound of peanuts? write the number sentence that goes with the word problem. Then, write your answer.
Answers
Answer:
Fred paid 70 cents per pound.
Step-by-step explanation:
Let c = the cost of one pound of peanuts.
[tex]4.5c = 3.15[/tex]
[tex]c = .70[/tex]
Answer:0.7
Step-by-step explanation:
3.15÷4.5=0.7
If the distance a runner travels is represented by d(h) = 2√h and the associated time is t(h) = 3√/4h, what is the runner's speed?
s(h) = h√3
s(h) =1/3
s(h) = 12h
s(h) = √ 2/h
Answers
Based on the given distance and time, the speed of the runner is s(h) = 8h/√3.
Relationship between time, distance and speed:
The relationship of speed with distance and time is written as,
Speed = Distance x Time
Which describes the distance travelled divided by the time taken to cover the distance will results the speed.
Given,
Here we need to find the runner's speed when the distance a runner travels is represented by d(h) = 2√h and the associated time is t(h) = 3√/4h.
We know that the formula to calculate the speed is,
Speed = Distance / Time
Here we have the value of
distance = d(h) = 2√h
time = t(h) = √3/4h
Now, we have to apply the values on the formula, then we get,
Speed = 2√h / √3/4h
Therefore, the speed of the runner is 8h/√3.
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solve the quadratic equation 3x^2+x-5=0 give your answer to 2 significant figures
Answers
The resultant answer of the given quadratic equation is x₁,₂ = -1 ± √61/6.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a, and b are the coefficients, and c is the constant term.So, solve 3x²+x-5=0 as follows:
Quadratic formula: x = -b ± √b²-4ac/2aNow, evaluate as follows:
x = -b ± √b²-4ac/2ax₁,₂ = -1 ± √1² - 4×3(-5)/2×3x₁,₂ = -1 ± √61/2×3x₁,₂ = -1 ± √61/6Therefore, the resultant answer of the given quadratic equation is x₁,₂ = -1 ± √61/6.
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Can you please help me out with a question
Answers
What is the value for y?
Answers
Answer:
28
Step-by-step explanation:
x - 5 = 34, meaning 39 = x
34 + 34 = 68
All triangles add up to 180
180 - 68 = 112
112/4 = 28
2. MGSE9-12.A.REI. 1 Which step in solving this equation is justified by the Distributive Property? Consider the sequence of steps to solve the equation: 6v + 3(v – 5) = 4v - (2v + 1) Given = 6v + 3(v — 5) = 4v - (2v + 1) Step 1 = 6 + 3x – 15 = 4y - (2v + 1) Step 2 => 6v + 3v – 15 = 4v – 2y = 1 Step 3 9v – 15 = 4y – 2y - 1 Step 4 => 9v - 15 -- 2v + 4y = 1 Step 5 =9v = 15 = 2y + 1 Step 6 3 7v - 15 =-1 Step 7 3 Tv = 14 Step 8 = v= 2 a. Step 1 b. Step 7 C. Step 5 d. Step 2
Answers
6v + 3(v – 5) = 4v - (2v + 1)
Given = 6v + 3(v — 5) = 4v - (2v + 1)
step 1
when you open the first parenthsesis in step 1
we have 6v + 3v - 15 = 4v - (2v + 1)
Then in step 2
we open the second parenthesis,
This gives;
6v + 3v - 15 = 4v - 2v - 1
Therefore; step 1 and step 2 justified the distributive property
Given ∠3≅∠13, which lines, if any, must be parallel based on the given information? Justify your conclusion. Responses a∥b, Converse of the Alternate Interior Angles Theorem a is parallel to b, , Converse of the Alternate Interior Angles Theorem c∥d, Converse of the Same-Side Interior Angles Theorem c is parallel to d, , Converse of the Same-Side Interior Angles Theorem c∥d, Converse of the Corresponding Angles Theorem c is parallel to d, , Converse of the Corresponding Angles Theorem not enough information to make a conclusion not enough information to make a conclusion Two horizontal, parallel lines, line c and line d, where line c is above line d. These lines are intersected by two diagonal parallel lines, line a and line b. Line a is to the left of line b. The angles created by each intersection are numbered. From top left, going clockwise, the angles where line a intersects line c are labeled eleven, ten, nine, and twelve. The angles where line b intersects line c are labeled seven, six, five, and eight. The angles where line a intersects line d are labeled fifteen, fourteen, thirteen and sixteen. The angles where line b intersects line d are labeled three, two, one and four.
Answers
The order of the arrangement of the angles in the question (see attached drawing based on a similar question on the website, created with MS Word) indicate that the angles ∠3 and ∠13 are congruent. The correct option is therefore;
a║b, Converse of the Alternate Interior Theorem
What are congruent angles?Congruent angles are angles that have the same measure.
The lines that must be parallel, such that ∠3 ≅ ∠13 is indicated by the definition of the relationship between ∠3 and ∠13 as follows;
Statement [tex]{}[/tex] Reason
1. ∠3 ≅ ∠13 [tex]{}[/tex] 1. Given
2. ∠3 and ∠13 are alt int. ∠s[tex]{}[/tex] between a and b 2. Definition
3. Line a is parallel to line b [tex]{}[/tex] 3. Conv of the alt int. ∠s theorem
The lines that must be parallel are line a and line bThe reason for the conclusion is based on the converse of the alternate interior angles theorem as follows;
Angle ∠3 and angle ∠13 are alternate interior angles, which are angles located on the inside and on the opposite sides of the common transversal of two lines.
The converse of the alternate interior angles theorem state that if the alternate interior angles formed between two lines, a and b and their common transversal are congruent, then the two lines, a and b are parallel (a ║ b).
The correct option is therefore;
a ║ b, Converse of the Alternate Interior Angles Theorem
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Find the exponential equation that goes through the points (-1, 2) and (2, 128) Bullet point 3
Answers
The general form of the exponential function is given by;
[tex]y=f(x)=ab^x[/tex]where a is the initial value and b is any value greater than 0.
If the exponential function goes through the points (-1, 2) and (2, 128) we have;
[tex]2=ab^{-1}\ldots\ldots\ldots\text{.}.1[/tex]And,
[tex]128=ab^2\ldots\ldots\ldots\text{.}.2[/tex]Divide [2] by [1] we have;
[tex]\frac{128}{2}=\frac{ab^2}{ab^{-1}}[/tex]Simplify
[tex]\begin{gathered} 64=\frac{b^2}{b^{-1}} \\ 64=b^2\div b^{-1} \\ 64=b^{2--1} \\ 64=b^{2+1} \\ 64=b^3 \end{gathered}[/tex]Find the cube-root of both sides
[tex]\begin{gathered} \sqrt[3]{64}=\sqrt[3]{b^3} \\ 4=b \\ \therefore b=4 \end{gathered}[/tex]Substitute the value of b = 4 in [2] we get;
[tex]\begin{gathered} 128=ab^2 \\ 128=a(4)^2 \\ 128=16a \\ \text{Divide both sides by 16} \\ \frac{128}{16}=\frac{16a}{16} \\ 8=a \\ \therefore a=8 \end{gathered}[/tex]Substitute the value of a and b in
[tex]f(x)=ab^x[/tex]then we have;
[tex]f(x)=8(4)^x[/tex]Therefore, the exponential function that goes through the points ( -1, 2) and (2, 128) is;
[tex]f(x)=8(4)^x[/tex]What is the range of this relation?
Answers
Answer: (-9, -3, -2, 6, 8)
Step-by-step explanation: