AnswersAlgebraic ReasoningUsing Exponential Functions

Using Exponential Functions — Quiz Answers

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Determine which of the following graphs represent the equation. Also determine the y -intercept of the graph. y is equal to 5 times open paren 2 to the x th power close paren

A
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right. The y-intercept of the graph is 1. y -intercept is equal to 1
B
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 4 comma 0 point 3 1), (negative 3 comma 0 point 6 2 5), (negative 2 comma 1 point 2 5), (negative 1 comma 2 point 5), and (0 comma 5). The y-intercept of the graph is 5. y -intercept is equal to 5
C
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right. The y-intercept of the graph is 2. y -intercept is equal to 2
D
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 2 comma 0 point 2 5), (negative 1 comma 0 point 5), (0 comma 1), (1 comma 2), and (2 comma 4). The y-intercept of the graph is 1. y -intercept is equal to 1
2
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Determine which of the following graphs represent the equation. Also determine the y -intercept of the graph. y is equal to 3 times open paren 2 to the x th power close paren

A
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 3 comma 0 point 0 7 4), (negative 2 comma 0 point 2 2), (negative 1 comma 0 point 6 6), and (0 comma 2). The y-intercept of the graph is 2. y -intercept is equal to 2
B
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 3 comma 0 point 1 2 5), (negative 2 comma 0 point 2 5), (negative 1 comma 0 point 5), and (0 comma 1). The y-intercept of the graph is 1. y -intercept is equal to 1
C
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 4 comma 0 point 1 8 7 5), (negative 3 comma 0 point 3 7 5), (negative 2 comma 0 point 7 5), (negative 1 comma 1 point 5), and (0 comma 3). The y-intercept of the graph is 3. y -intercept is equal to 3
D
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 2 comma 0 point 0 6 2 5), (negative 1 comma 0 point 1 2 5), and (0 comma 1). The y-intercept of the graph is 1. y -intercept is equal to 1
3

Given the table, 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 of x 0 2 4 6 8

A
Linear; y is equal to x
B
Linear; y is equal to 2 x
C
Exponential; y is equal to 1 times 1 point 2 to the x th power
D
Exponential; y is equal to 2 times 1 point 1 to the x th power
4

Determine which of the following graphs represent the equation. Also determine the y -intercept of the graph. y is equal to 4 times open paren 2 to the x th power close paren

A
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 4 comma 0 point 2 5), (negative 3 comma 0 point 5), (negative 2 comma 1), (negative 1 comma 2), and (0 comma 4). The y-intercept of the graph is 4. y -intercept is equal to 4
B
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 2 comma 0 point 0 6 2 5), (negative 1 comma 0 point 1 2 5), and (0 comma 1). The y-intercept of the graph is 1. y -intercept is equal to 1
C
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 2 comma 0 point 1 2 5), (negative 1 comma 0 point 5), and (0 comma 2). The y-intercept of the graph is 2. y -intercept is equal to 2
D
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 3 comma 0 point 1 2 5), (negative 2 comma 0 point 2 5), (negative 1 comma 0 point 5), and (0 comma 1). The y-intercept of the graph is 1. y -intercept is equal to 1
5

Given the table, 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 of x 18 14 10 6 2

A
Exponential; y is equal to 22 point 5 times 0 point 4 1 to the x th power
B
Exponential; y is equal to 22 point 5 times 0 point 5 9 raised to the x power
C
Linear; negative 4 x plus 18
D
Linear; y is equal to 18 x minus 4
6

Given the table, 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 of x 12 point 5 13 point 7 5 15 point 1 2 5 16 point 6 3 8 18 point 3 0 1

A
Linear; y is equal to 1 point 4 9 9 x plus 12 point 3 6 4 8
B
Exponential; y is equal to 12 point 5 times 1 point 1 0 to the x th power
C
Exponential; y is equal to 1 point 1 0 times 12 point 5 to the x th power
D
Linear; 12 point 3 6 4 8 x plus 1 point 4 9 9
7

Given the table, 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 of x 14 12 point 6 11 point 3 4 10 point 2 0 6 9 point 1 8 5

A
Exponential; y is equal to 14 times 0 point 1 0 to the x th power
B
Exponential; y is equal to 14 times 0 point 9 0 to the x th power
C
Linear; y is equal to negative 1 point 2 0 2 4 x plus 13 point 8 7 1
D
Linear; 18 point 8 7 1 x minus 1 point 2 0 2 4
8

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
9

From the table, determine whether the data shows an exponential function. Explain why or why not. x negative 5 negative 4 negative 3 negative 2 y 0 point 5 2 8 32

A
Yes; the domain values are at regular intervals and the range values have a common factor 4 .
B
No; 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
Yes; the domain values are at regular intervals and the range values have a common factor 8 .
10

From the table, determine whether the data shows an exponential function. Explain why or why not. x 3 2 1 negative 1 y 8 2 0 point 5 0 point 1 2 5

A
Yes; the domain values are at regular intervals and the range values have a common factor 4 .
B
No; the domain values are at regular intervals and the range values have a common factor 0 point 2 5 .
C
No; the domain values are not at regular intervals although the range values have a common factor.
D
Yes; the domain values are at regular intervals and the range values have a common factor 0 point 2 5 .
11

From the table, determine whether the data shows an exponential function. Explain why or why not. x 3 6 9 12 y 1 2 4 8

A
No; a different value is added to each range value.
B
Yes; the domain values are at regular intervals and the range values have a common factor 2 .
C
No; the domain values are at regular intervals.
D
No; there is no relationship between the x value and its corresponding y value.
12

Given the table, 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 of x 14 12 point 6 11 point 3 4 10 point 2 0 6 9 point 1 8 5

A
Exponential; y is equal to 14 times 0 point 9 0 to the x th power
B
Exponential; y is equal to 14 times 0 point 1 0 to the x th power
C
Linear; y is equal to negative 1 point 2 0 2 4 x plus 13 point 8 7 1
D
Linear; 18 point 8 7 1 x minus 1 point 2 0 2 4
13

Determine which of the following graphs represent the equation. Also determine the y -intercept of the graph. y is equal to 4 times open paren 2 to the x th power close paren

A
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 3 comma 0 point 1 2 5), (negative 2 comma 0 point 2 5), (negative 1 comma 0 point 5), and (0 comma 1). The y-intercept of the graph is 1. y -intercept is equal to 1
B
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 2 comma 0 point 1 2 5), (negative 1 comma 0 point 5), and (0 comma 2). The y-intercept of the graph is 2. y -intercept is equal to 2
C
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 4 comma 0 point 2 5), (negative 3 comma 0 point 5), (negative 2 comma 1), (negative 1 comma 2), and (0 comma 4). The y-intercept of the graph is 4. y -intercept is equal to 4
D
Image with description A coordinate plane has an x-axis ranging from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. The graph increases as x values move from left to right and the graph passes through the points (negative 2 comma 0 point 0 6 2 5), (negative 1 comma 0 point 1 2 5), and (0 comma 1). The y-intercept of the graph is 1. y -intercept is equal to 1
14

If 5000 dollars is invested at an interest rate of 4 percent each year, what is the value of the investment in 5 years? Write an exponential function and solve.

A
y is equal to 5000 times 1 point 0 4 to the 5th power ; 6083 point 2 6 dollars
B
y is equal to 1 point 0 4 times 5000 to the 5th power ; 6830 point 2 6 dollars
C
y is equal to 5 times 5000 raised to the 1 point 0 4 power ; 35 dollars comma 147 point 8 5
D
y is equal to 5000 times 5 raised to the 1 point 0 4 power ; 26 dollars comma 662 point 3 7
15

Given the table, 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 of x 0 2 4 6 8

A
Exponential; y is equal to 1 times 1 point 2 to the x th power
B
Exponential; y is equal to 2 times 1 point 1 to the x th power
C
Linear; y is equal to 2 x
D
Linear; y is equal to x
16

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
17

Given the table, 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 of x 12 point 5 13 point 7 5 15 point 1 2 5 16 point 6 3 8 18 point 3 0 1

A
Linear; 12 point 3 6 4 8 x plus 1 point 4 9 9
B
Exponential; y is equal to 12 point 5 times 1 point 1 0 to the x th power
C
Exponential; y is equal to 1 point 1 0 times 12 point 5 to the x th power
D
Linear; y is equal to 1 point 4 9 9 x plus 12 point 3 6 4 8
18

Given the table, 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 of x 18 14 10 6 2

A
Linear; y is equal to 18 x minus 4
B
Exponential; y is equal to 22 point 5 times 0 point 5 9 raised to the x power
C
Linear; negative 4 x plus 18
D
Exponential; y is equal to 22 point 5 times 0 point 4 1 to the x th power
19

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 negative real numbers
B
T-chart using random values for x and y
C
T-chart using all real numbers
D
T-chart using positive real numbers
20

Given the table, 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 of x 12 point 5 13 point 7 5 15 point 1 2 5 16 point 6 3 8 18 point 3 0 1

A
Linear; 12 point 3 6 4 8 x plus 1 point 4 9 9
B
Linear; y is equal to 1 point 4 9 9 x plus 12 point 3 6 4 8
C
Exponential; y is equal to 1 point 1 0 times 12 point 5 to the x th power
D
Exponential; y is equal to 12 point 5 times 1 point 1 0 to the x th power

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