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

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

Question 1

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

Accepted Answer

$$f(x) = a \cdot b^x$$, 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

$$10.5$$

Question 3

Which of the following tables represents an exponential function?

Accepted Answer

A table where the $$y-$$values are multiplied by a constant factor as $$x$$ increases by 1.

Question 4

A town has a population of 1000 people at time $$t = 0. $$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 5

Which graph best represents exponential decay?

Accepted Answer

A curve that decreases rapidly and approaches $$y = 0 as$$ $$x$$ increases.

Question 6

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

Accepted Answer

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

Question 7

Which transformation shifts the graph of $$f(x) = 2^x up by 3 $$units?

Accepted Answer

$$f(x) = 2^x + 3$$

Question 8

What is the $$y-$$intercept of the function $$f(x) = 5 \cdot 3^x$$?

Accepted Answer

$$5$$

Question 9

If $$f(x) = 2^x$$ and $$g(x) = 2$$^{x-4}$$, how is the graph of g(x$$)$$ transformed from f(x$$)$$?

Accepted Answer

Shifted right by 4 units

Question 10

Which of the following is NOT an exponential function?

Accepted Answer

$$f(x) = x^2$

Question 11

A bacteria culture triples every hour. If $$N(t) is $$the number of bacteria after $$t$$ hours, which function models this situation?

Accepted Answer

$$N(t) = N_0$ \cdot 3^t$$

Question 12

What is the domain and range of $$f(x) = 2^x$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(0, \infty)$$

Question 13

Which of the following describes the horizontal asymptote of $$f(x) = 4^x + 2$$?

Accepted Answer

$$y = 2$$

Question 14

If $$f(x) = 2^x is $$reflected over the $$x-$$axis, what is the new function?

Accepted Answer

$$f(x) = -2^x$$

Question 15

A population decreases by 12% per year. If the initial population is $$P_0$$, which function models the population after $$t$$ years?

Accepted Answer

$$P(t) = P_0$ \cdot (1 - 0.12)^t$$

Question 16

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

Accepted Answer

$$4 \cdot 2^x$$

Question 17

If $$f(x) = 3^x$$ and $$g(x) = 2 \cdot 3^x$$, how does the graph of $$g(x)$$ compare to $$f(x)$$?

Accepted Answer

It is stretched vertically by a factor of 2.

Question 18

Which of the following functions represents exponential growth?

Accepted Answer

$$f(x) = 5 \cdot 1.2^x$$

Question 19

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

Accepted Answer

It represents exponential decay.

C2,C3

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