Question 1

A radioactive substance decays according to $$A = A_0$ e$$^{kt}$$, where k$$ \u003c 0$$. If the half-life of the substance is 20 years, what is the value of k$?

Accepted Answer

$$k = \frac{\ln(1/2)}{20}$$

Question 2

Which of the following is the correct domain for the function $$y = \log(x + 5)$$?

Accepted Answer

$$x \u003e -5$$

Question 3

A population of bacteria grows according to $$P(t) = 500e$$^{0.04t}$$. How long will it take for the population to double?

Accepted Answer

$$t = \frac{\ln(2)}{0.04}$$

Question 4

Which property of logarithms allows you to write $$\log_b(MN) as$$ $$\log_b(M) + \log_b(N)$$?

Accepted Answer

Product Rule

Question 5

Given $$y = a b^x$$, which value of $$b$$ represents exponential decay?

Accepted Answer

$$0 \u003c b \u003c 1$$

Question 6

If $$f(x) = 3\ln(x)$$, what is the average rate of change of $$f$$ from $$x = 1 to$$ $$x = 2$$?

Accepted Answer

$$\frac{3\ln(2) - 3\ln(1)}{2 - 1}$$

Question 7

A medication’s concentration in the bloodstream decreases by 15% per hour. If the initial concentration is $$C_0$$, what is the concentration after 3 hours?

Accepted Answer

$$C_0$$ 	imes $$0.85^3$$

Question 8

Which of the following is the correct change of base formula for logarithms?

Accepted Answer

$$\log_b(M) = \frac{\log(M)}{\log(b)}$$

Question 9

Suppose $$V(t) = 7e$$^{-0.16t}$$ models the voltage decay in a circuit. What is the percent decrease per second?

Accepted Answer

$$1 - e$$^{-0.16}$$

Question 10

Which of the following statements about the graph of $$y = \log(x) is $$true?

Accepted Answer

Its domain is $$x \u003e 0$$

Question 11

If $$A = Pe$$^{rt}$$ represents continuous compounding, what does r$ represent?

Accepted Answer

The rate (as a decimal)

Question 12

Which step is NOT part of the standard process for solving exponential equations using logarithms?

Accepted Answer

Multiply both sides by the exponent

Question 13

Given $$y = \log(x + 11)$$, what is the vertical asymptote of the graph?

Accepted Answer

$$x = -11$$

Question 14

A chemical reaction follows $$C(t) = 100e$$^{-0.05t}$$. How long until only 25% of the initial concentration remains?

Accepted Answer

$$t = \frac{\ln(0.25)}{-0.05}$$

Question 15

Which of the following is the correct power rule for logarithms?

Accepted Answer

$$\log_b(M^n) = n \log_b(M)$$

Question 16

If $$y = ab^x$$ and $$b = 1 + r$$ for growth, what does $$r$$ represent?

Accepted Answer

The percent increase per period (as a decimal)

Question 17

Which of the following is true about the range of an exponential function $$y = a b^x$$?

Accepted Answer

$$(0, \infty)$$

Question 18

A scientist models the growth of a cell culture with $$N(t) = 2000e$$^{0.03t}$$. What is the average rate of change of N$ from t = 0$ to t = 10$?

Accepted Answer

$$\frac{2000e$$^{0.3}$$ - 2000}{10}$$

Question 19

Which of the following is NOT a feature of the graph of $$y = e^x$$?

Accepted Answer

Vertical asymptote at $$x = 0$$

Exponential and Logarithmic Models: Concepts, Properties, and Applications

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드