Question 1

Which of the following is the correct exponential function for the graph that passes through the points $$(0,1)$$, $$(1,2)$$, $$(2,4)$$, and $$(3,8)$$?

Accepted Answer

$$y = 2^x$$

Question 2

Given the exponential function $$f(x) = 2^x$$, what is the horizontal asymptote of its graph?

Accepted Answer

$$y = 0$$

Question 3

Which of the following points does NOT lie on the graph of $$y = 6^x$$?

Accepted Answer

$$(1,4)$$

Question 4

If the base $$b of an $$exponential function $$y = b^x is $$between $$0$$ and $$1$$, which statement is true about the function?

Accepted Answer

It is a decreasing function.

Question 5

What is the domain and range of the function $$y = e^x$$?

Accepted Answer

Domain: $$x \in (-\infty, \infty)$$; Range: $$y \in (0, \infty)$$

Question 6

Which real-life scenario is best modeled by an exponential function?

Accepted Answer

Population growth in a city

Question 7

If $$A = P(1 + \frac{r}{n}$$)^{nt}$$, what is the value of A$ after 5 years for a $$\$$10,000$$ deposit at $$9\%$ annual interest compounded monthly?

Accepted Answer

$$A \approx \15$$,656.81$

Question 8

Which of the following is NOT an exponential function?

Accepted Answer

$$g(x) = x^2$

Question 9

What is the value of $$f(x) = 3.2^x$$ when $$x = 5$$? (Round to two decimal places)

Accepted Answer

$$f(5) \approx 335.54$$

Question 10

If $$A = Pe$$^{rt}$$, what is the balance after 3 years for a $$\$$2340$$ deposit at $$3.1\%$ annual interest compounded continuously?

Accepted Answer

$$A \approx \2$$,568.06$

Question 11

Which exponential rule allows you to simplify $$a^n \cdot a^m$$?

Accepted Answer

Product Rule: $$a^n \cdot a^m = a$$^{n+m}$$

Question 12

What is the value of $$64^{\frac{2}$${3}}$$?

Accepted Answer

Question 13

Which graph represents a decreasing exponential function?

Accepted Answer

A graph of $$y = \frac{1}{2}^x$$

Question 14

If $$f(x) = b^x$$ and $$b \u003e 1$$, which of the following statements is true?

Accepted Answer

The function is increasing.

Question 15

What is the value of $$e$$ rounded to five decimal places?

Accepted Answer

$$e \approx 2.71828$$

Question 16

If you invest $$\2$$,100$$ at an annual interest rate of 5$$\%$$ compounded continuously for 6$ years, what is the final amount?

Accepted Answer

$$A \approx \2$$,828.13$

Question 17

Which of the following is the correct formula for compound interest compounded $$n$$ times per year?

Accepted Answer

$$A = P(1 + \frac{r}{n}$$)^{nt}$$

Question 18

If $$f(x) = 2^x$$, what is $$f(-2)$$?

Accepted Answer

$$\frac{1}{4}$$

Question 19

Which of the following is a characteristic of all exponential functions $$y = b^x$$ where $$b \u003e 0$$ and $$b 
eq 1$$?

Accepted Answer

The range is $$y \in (0, \infty).$$

Exponential and Logarithmic Functions: Core Concepts and Applications

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