AnswersApplications and ModelingUse Exponential Functions

Use Exponential Functions Answers

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Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function. x 0 1 2 3 4 f (x) 12.5 13.75 15.125 16.638 18.301

Question illustration
A
Exponential;
B
Linear; y = 1.499x + 12.3648
C
Exponential;
D
Linear; 12.3648x + 1.499
2
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If $5000 is invested at an interest rate of 4% each year, what is the value of the investment in 5 years? Write an exponential function and solve.

Question illustration
A
;$6083.26
B
;$26,662.37
C
;$6830.26
D
;$35,147.85
3

From the table below, determine whether the data shows an exponential function. Explain why or why not. x31-1-3y1234

A
No; the domain values are at regular intervals and the range values have a common sum 1.
B
No; the domain values are not at regular intervals.
C
Yes; the domain values are at regular intervals and the range values have a common factor 2.
D
Yes; the domain values are at regular intervals and the range values have a common sum 1.
4

A guest on a talk show tends to receive many phone calls right after she is on the show, and then the calls become less frequent. This can be represented by the equation y = 30(0.92)d, where y is the number of phone calls after d days. How many phone calls should she expect after a week?

A
28
B
23
C
17
D
2
5

Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function. x 0 1 2 3 4 f(x) 0 2 4 6 8

Question illustration
A
Exponential;
B
Linear; y = 2x
C
Exponential;
D
Linear; y = x
6

Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function. x 0 1 2 3 4 f(x) 0 2 4 6 8

Question illustration
A
Exponential;
B
Linear; y = 2x
C
Exponential;
D
Linear; y = x
7

Determine which of the following graphs represent the equation below. Also determine the y-intercept of the graph.

Question illustration
A
y-intercept = 3
B
y-intercept = 1
C
y-intercept = 1
D
y-intercept = 2
8

From the table below, determine whether the data shows an exponential function. Explain why or why not. x321–1y820.50.125

A
No; the domain values are at regular intervals and the range values have a common factor 0.25.
B
No; the domain values are not at regular intervals although the range values have a common factor.
C
Yes; the domain values are at regular intervals and the range values have a common factor 4.
D
Yes; the domain values are at regular intervals and the range values have a common factor 0.25.
9

What is the y-intercept of the graph of y = 2.5x?

A
2.5
B
1
C
0
D
-1
10

Exponential functions exhibit exponential growth (or decay). What does this mean to the graphs of these functions?

A
the graph will rise or fall more dramatically than a polynomial graph
B
the graph is three dimensional
C
the graphs represent the population of bacteria in your mouth
D
the exponent in the equation is less than one
11

Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function. x 0 1 2 3 4 f (x) 14 12.6 11.34 10.206 9.185

Question illustration
A
Exponential;
B
Linear; y = -1.2024x + 13.871
C
Exponential;
D
Linear; 18.871x - 1.2024
12

Determine which of the following graphs represent the equation below. Also determine the y-intercept of the graph.

Question illustration
A
y-intercept = 4
B
y-intercept = 2
C
y-intercept = 1
D
y-intercept = 1
13

To graph an exponential, you need to plot a few points, and then connect the dots and draw the graph. Where do you come up with values to use in the graph?

A
T-chart using positive real numbers
B
T-chart using negative real numbers
C
T-chart using all real numbers
D
T-chart using random values for x and y
14

Determine which of the following graphs represent the equation below. Also determine the y-intercept of the graph.

Question illustration
A
y-intercept = 1
B
y-intercept = 2
C
y-intercept = 1
D
y-intercept = 5
15

From the table below, determine whether the data shows an exponential function. Explain why or why not. x –5 –4 –3 –2 y 0.5 2 8 32

A
Yes; the domain values are at regular intervals and the range values have a common factor 8.
B
Yes; the domain values are at regular intervals and the range values have a common factor 4.
C
No; the domain values are not at regular intervals.
D
No; the domain values are at regular intervals and the range values have a common factor 4.
16

From the table below, determine whether the data shows an exponential function. Explain why or why not. x36912y1248

A
No; the domain values are at regular intervals.
B
No; a different value is added to each range value.
C
No; there is no relationship between the x value and its corresponding y value.
D
Yes; the domain values are at regular intervals and the range values have a common factor 2.
17

Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function. x 0 1 2 3 4 f (x) 18 14 10 6 2

Question illustration
A
Exponential;
B
Linear; y = 18x - 4
C
Exponential;
D
Linear; -4x + 18

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