Q: Which of the following is the correct general form of an exponential function?

$$f(x) = ab^x$$, where $$a \, \neq \, 0$$ and $$b \u003e 0, \, b \, \neq \, 1$$

Q: Which of the following best describes the end behavior of the exponential decay function $$f(x) = 2 \cdot (0.5)^x$$?

$$f(x) \to 0 as$$ $$x \to \infty$$

Question 1

Which of the following is the correct general form of an exponential function?

Accepted Answer

$$f(x) = ab^x$$, where $$a \, 
eq \, 0$$ and $$b \u003e 0, \, b \, 
eq \, 1$$

Question 2

Given the function $$f(x) = 3 \cdot 2^x$$, what is the average rate of change from $$x = 1 to$$ $$x = 4$$?

Accepted Answer

$$7.5$$

Question 3

Which of the following functions is NOT an exponential function?

Accepted Answer

$$f(x) = x^2$

Question 4

A population of bacteria triples every hour. Which function models the number of bacteria after $$t$$ hours if the initial population is $$200$$?

Accepted Answer

$$f(t) = 200 \cdot 3^t$$

Question 5

Which of the following tables represents an exponential function?

Accepted Answer

x: 0, 1, 2, 3; f(x): 2, 4, 8, 16

Question 6

If $$f(x) = 2^x$$, which transformation results in $$g(x) = 2$$^{x-3}$$ + 4$$?

Accepted Answer

Shift right 3 units and up 4 units

Question 7

Given two points $$(2, 12)$$ and $$(4, 27)$$, what is the exponential function $$y = ab^x$$ passing through these points?

Accepted Answer

$$y = 3 \cdot (\frac{3}{2})^x$$

Question 8

Which of the following best describes the end behavior of the exponential decay function $$f(x) = 2 \cdot (0.5)^x$$?

Accepted Answer

$$f(x) 	o 0 as$$ $$x 	o \infty$$

Question 9

A town has a population of $$1000$$ people at time $$t = 0. If $$the population increases by $$5\%$$ per year, which function models the population after $$t$$ years?

Accepted Answer

$$P(t) = 1000 \cdot (1.05)^t$$

Question 10

Which of the following statements is TRUE about the graph of $$y = ab^x$$ when $$0 \u003c b \u003c 1$$?

Accepted Answer

It represents exponential decay.

Question 11

If $$f(x) = 2^x$$ and $$g(x) = 2$$^{x+2}$$, how is the graph of g(x$$)$$ related to f(x$$)$$?

Accepted Answer

It is shifted 2 units left.

Question 12

Which of the following is the $$y-$$intercept of the function $$f(x) = 3 \cdot 2^x + 5$$?

Accepted Answer

$$8$$

Question 13

A certain radioactive substance decays by $$12\%$$ each year. If the initial amount is $$A_0$$, which function models the amount after $$t$$ years?

Accepted Answer

$$A(t) = A_0$ \cdot (0.88)^t$$

Question 14

Which of the following is the equation of the horizontal asymptote for $$f(x) = 4 \cdot 3^x - 2$$?

Accepted Answer

$$y = -2$$

Question 15

Suppose $$f(x) = 5 \cdot 2^x. $$What is $$f(3)$$?

Accepted Answer

$$40$$

Question 16

Which of the following best describes the difference between a linear and an exponential function based on their tables of values?

Accepted Answer

Linear functions have constant differences; exponential functions have constant ratios.

Question 17

If $$f(x) = 2^x$$ and $$g(x) = -2^x$$, how is the graph of $$g(x)$$ related to $$f(x)$$?

Accepted Answer

It is reflected over the $$x-$$axis.

Question 18

Which of the following is equivalent to $$2^{3x}$$?

Accepted Answer

$$(2^3)^x$

Question 19

Given $$f(x) = 3 \cdot 5^x$$, what is the effect of replacing $$x$$ with $$x-2 in $$the function?

Accepted Answer

The graph shifts right 2 units.

Question 20

Which of the following functions represents exponential growth?

Accepted Answer

$$f(x) = 7 \cdot (1.2)^x$$

C2-C3

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