AP Precalculus: Exponential and Logarithmic Functions flashcards

Question 1

What is the common logarithm of x?

Accepted Answer

The power you raise 10 to in order to get x; it is written log(x), short for log_10(x).

Question 2

What is the natural logarithm of x?

Accepted Answer

The power you raise e to in order to get x; it is written ln(x), short for log_e(x).

Question 3

In y = log_b(x), what does y represent?

Accepted Answer

The power to which the base b is raised to produce x.

Question 4

What does the change-of-base formula let you do?

Accepted Answer

Rewrite a logarithm in any base as a quotient of logarithms in some other base.

Question 5

In words, what does the product rule for logarithms say?

Accepted Answer

The log of a product equals the sum of the logs of the factors.

Question 6

In words, what does the quotient rule for logarithms say?

Accepted Answer

The log of a quotient equals the difference of the logs.

Question 7

What is compound interest?

Accepted Answer

Interest earned on the whole balance, not on the principal alone.

Question 8

What is doubling time?

Accepted Answer

How long it takes for a quantity to become twice as large.

Question 9

What is half-life?

Accepted Answer

How long it takes a decaying substance, decaying exponentially, to fall to half its starting amount.

Question 10

What is exponential growth?

Accepted Answer

Growth in which the rate of increase is proportional to the amount present.

Question 11

What is an extraneous solution?

Accepted Answer

A solution that arises while solving an equation but fails to meet the conditions of the original equation.

Question 12

What is another name for the nominal rate of an investment account?

Accepted Answer

Annual percentage rate (APR).

Question 13

What does Newton’s Law of Cooling describe?

Accepted Answer

An object's temperature as a function of time as it approaches the surrounding (ambient) temperature.

Question 14

In a logistic model, what is the carrying capacity?

Accepted Answer

The limiting value of the output.

Question 15

What conditions must the base b satisfy in the exponential function f(x) = b^x?

Accepted Answer

b > 0 and b ≠ 1.

Question 16

What is the compound interest formula for account value A(t)?

Accepted Answer

A(t) = P(1 + r/n)^(nt).

Question 17

In A(t) = P(1 + r/n)^(nt), what does n stand for?

Accepted Answer

How many times per year interest is compounded.

Question 18

In A(t) = P(1 + r/n)^(nt), what does P stand for?

Accepted Answer

The initial investment, often called the principal.

Question 19

What is the continuous growth formula?

Accepted Answer

A(t) = a·e^(rt), where a is the starting amount.

Question 20

To three decimal places, what is the value of e used in the continuous growth formula?

Accepted Answer

About 2.718.

Question 21

Write the product rule for logarithms as a formula.

Accepted Answer

log_b(xy) = log_b(x) + log_b(y).

Question 22

Write the quotient rule for logarithms as a formula.

Accepted Answer

log_b(x/y) = log_b(x) − log_b(y).

Question 23

Write the power rule for logarithms as a formula.

Accepted Answer

log_b(x^k) = k·log_b(x).

Question 24

Write the change-of-base formula for log_b(x) using a new base c.

Accepted Answer

log_b(x) = log_c(x) / log_c(b), with c > 0, c ≠ 1 and b ≠ 1.

Question 25

For A = A_0·e^(kt) with k < 0, what is the half-life t?

Accepted Answer

t = −ln(2) / k.

Question 26

For A = A_0·e^(kt) with k > 0, what is the doubling time t?

Accepted Answer

t = ln(2) / k.

Question 27

How are exponential and logarithmic functions related?

Accepted Answer

Each is the inverse of the other.

Question 28

What are the domain and range of y = log_b(x)?

Accepted Answer

Domain (0, ∞); range (−∞, ∞).

Question 29

What is the vertical asymptote of f(x) = log_b(x)?

Accepted Answer

The line x = 0.

Question 30

What are the domain and range of f(x) = b^x?

Accepted Answer

Domain (−∞, ∞); range (0, ∞).

AP Precalculus: Exponential and Logarithmic Functions flashcards

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