Question 1

Given the function $$f(x) = e^x + 6$$, which of the following correctly describes its domain?

Accepted Answer

$$(-\infty, \infty)$$

Question 2

For the function $$f(x) = e^x + 6$$, what is the equation of its horizontal asymptote?

Accepted Answer

$$y = 6$$

Question 3

What is the y-intercept of the function $$f(x) = e^x + 6$$?

Accepted Answer

$$7$$

Question 4

Which of the following is the correct range for $$f(x) = e$$^{-x}$$ + 3$$?

Accepted Answer

$$(3, \infty)$$

Question 5

What is the y-intercept of $$f(x) = e$$^{-x}$$ + 3$$?

Accepted Answer

$$4$$

Question 6

Express $$\log_b \frac{n}{s} as a $$difference of logarithms.

Accepted Answer

$$\log_b n - \log_b s$$

Question 7

Rewrite $$\ln x^9$ y^8$ z as a $$sum of multiples of logarithms.

Accepted Answer

$$9 \ln x + 8 \ln y + \ln z$$

Question 8

Solve for $$x in $$the equation $$e^x = 30. $$Round your answer to four decimal places.

Accepted Answer

$$x = 3.4012$$

Question 9

Solve for $$t in $$the equation $$e^t = 902. $$Round your answer to four decimal places.

Accepted Answer

$$t = 6.8046$$

Question 10

Write the equation $$10^{-3} = 0.001$ in equivalent logarithmic form.

Accepted Answer

$$\log_{10} (0.001) = -3$$

Question 11

Write $$\log_3$ 1 = 0 in $$equivalent exponential form.

Accepted Answer

$$3^0 = 1$

Question 12

If $$\log_4$ y = 3$$, what is the value of $$y$$?

Accepted Answer

$$y = 64$$

Question 13

If $$\log_b 8 = \frac{1}{3}$$, what is the value of $$b$$?

Accepted Answer

$$b = 64$$

Question 14

A population of bacteria grows according to $$P(t) = e^t + 6. $$What is the minimum possible population?

Accepted Answer

$$6$$

Question 15

Which transformation describes the change from $$y = e^x to$$ $$f(x) = e^x + 6$$?

Accepted Answer

Vertical shift up by 6 units

Question 16

Which transformation describes the change from $$y = e^x to$$ $$f(x) = e$$^{-x}$$ + 3$$?

Accepted Answer

Reflection across the y-axis and vertical shift up by 3 units

Question 17

A company models its revenue with $$R(x) = e^x + 6. $$What is the revenue when $$x = 0$$?

Accepted Answer

$$7$$

Question 18

Which of the following is the correct logarithmic property for $$\log_b (mn)$$?

Accepted Answer

$$\log_b m + \log_b n$$

Question 19

If $$e^t = 902$$, which of the following best describes the process to solve for $$t$$?

Accepted Answer

Take the natural logarithm of both sides: $$t = \ln 902$$

Question 20

A scientist records the concentration of a substance as $$C(x) = e$$^{-x}$$ + 3. $$What happens to the concentration as $$x$$ increases?

Accepted Answer

It approaches 3 from above

Business Calculus: Exponential and Logarithmic Functions Review

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