Q: Which of the following best describes the general form of an exponential function?

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

Q: If $$e \approx 2.71828$$, which of the following expressions best represents the value of $$e as$$ $$n$$ approaches infinity?

$$e = \lim_{n \to \infty} \left(1 + \frac{1}{n} \right)^n$$

Question 1

Which of the following best describes the general form of an exponential function?

Accepted Answer

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

Question 2

Suppose the function $$f(x) = 50 \cdot 1.5^x$$ models the population of a bacteria culture after $$x$$ hours. What is the population after 4 hours?

Accepted Answer

$$253$$

Question 3

Which of the following statements about the graph of $$f(x) = 2^x is $$TRUE?

Accepted Answer

The graph passes through the point $$(0, 1)$$

Question 4

Given the exponential function $$f(x) = 3^x$$, which transformation results in the graph of $$g(x) = 3$$^{x-2}$$?

Accepted Answer

A shift 2 units to the right

Question 5

The function $$f(x) = 120 \cdot e$$^{0.03x}$$ models the value of a car in dollars, x$ years after purchase. What is the value of the car after 10 years? (Round to the nearest dollar.)

Accepted Answer

$$162$$

Question 6

Which of the following is the correct formula for the balance $$A in an $$account with principal $$P$$, annual interest rate $$r$$, compounded $$n$$ times per year for $$t$$ years?

Accepted Answer

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

Question 7

A sum of $$5,000 is invested at an annual rate of 6$$\%$$ compounded monthly. What is the balance after 3 years? (Use A = P$$ \left(1 + \frac{r}{n} \$$right)^{nt}$ and round to the nearest cent.)

Accepted Answer

$$5,955.04$$

Question 8

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

Accepted Answer

$$y = 0$$

Question 9

If $$e \approx 2.71828$$, which of the following expressions best represents the value of $$e as$$ $$n$$ approaches infinity?

Accepted Answer

$$e = \lim_{n 	o \infty} \left(1 + \frac{1}{n} ight)^n$$

Question 10

A sum of $$8,000 is invested at an annual rate of 5$$\%$$ compounded continuously. What is the balance after 7 years? (Use A$$ = $$Pe^{rt}$ and round to the nearest cent.)

Accepted Answer

$$11,349.94$$

Question 11

Which of the following real-world scenarios can be best modeled by an exponential function?

Accepted Answer

The growth of a population of bacteria in a petri dish

Question 12

If the graph of $$f(x) = 2^x is $$shifted 3 units up, what is the equation of the new function?

Accepted Answer

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

Question 13

A radioactive substance decays according to the function $$N(t) = 1000 \cdot e$$^{-0.05t}$$, where t$ is in years. How much of the substance remains after 10 years? (Round to the nearest whole number.)

Accepted Answer

$$607$$

Question 14

Which of the following is NOT a characteristic of the graph of an exponential function $$f(x) = b^x$$ with $$b \u003e 1$$?

Accepted Answer

The graph is symmetric about the $$y-$$axis

Question 15

If $$f(x) = 5^x$$ and $$g(x) = 5$$^{x+2}$$, how does the graph of g(x$$)$$ relate to the graph of f(x$$)$$?

Accepted Answer

It is shifted 2 units to the left

Question 16

A sum of $$12,000 is $$invested at an annual rate of $$7\%$$ compounded semiannually. What is the balance after 6 years? (Use $$A = P \left(1 + \frac{r}{n} \$$right)^{nt}$$ and round to the nearest cent.)

Accepted Answer

$$18,187.13$$

Exponential Functions and Their Applications

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