Precalculus: Exponential and Logarithmic Functions flashcards

Question 1

In f(x) = b^x, what conditions must the base b meet?

Accepted Answer

b > 0 and b ≠ 1

Question 2

What is the range of f(x) = b^x?

Accepted Answer

(0, ∞)

Question 3

Is f(x) = b^x increasing or decreasing when 0 < b < 1?

Accepted Answer

Decreasing

Question 4

What is the compound interest formula?

Accepted Answer

A(t) = P(1 + r/n)^(nt), with principal P, annual rate r, n compounding periods per year, t years

Question 5

What is the continuous growth formula?

Accepted Answer

A(t) = ae^(rt), where a is the starting amount

Question 6

What is the decimal approximation of e?

Accepted Answer

e ≈ 2.718282

Question 7

What is compound interest?

Accepted Answer

Interest paid on the entire balance rather than on the principal alone

Question 8

For x > 0, b > 0, b ≠ 1, what does y = log_b(x) mean?

Accepted Answer

b^y = x

Question 9

What is the common logarithm?

Accepted Answer

The logarithm with base 10, written log(x)

Question 10

What is the natural logarithm?

Accepted Answer

The logarithm with base e, written ln(x)

Question 11

What is the inverse of an exponential function?

Accepted Answer

A logarithmic function

Question 12

What is the x-intercept of the graph of f(x) = log_b(x)?

Accepted Answer

(1, 0)

Question 13

What is the domain of f(x) = log_b(x)?

Accepted Answer

(0, ∞)

Question 14

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

Accepted Answer

x = 0

Question 15

State the product rule for logarithms.

Accepted Answer

log_b(MN) = log_b(M) + log_b(N)

Question 16

State the quotient rule for logarithms.

Accepted Answer

log_b(M/N) = log_b(M) - log_b(N)

Question 17

State the power rule for logarithms.

Accepted Answer

log_b(M^n) = n log_b(M)

Question 18

State the change-of-base formula.

Accepted Answer

log_b(M) = log_n(M) / log_n(b), where n > 0, n ≠ 1, b ≠ 1

Question 19

What does the one-to-one property of exponential functions say for b^S = b^T (b > 0)?

Accepted Answer

b^S = b^T exactly when S = T

Question 20

What is an extraneous solution?

Accepted Answer

A solution that comes up while solving an equation but does not satisfy the original equation

Question 21

What is half-life?

Accepted Answer

The time for a substance decaying exponentially to drop to half its original amount

Question 22

For A = A0 e^(kt) with k < 0, what is the half-life?

Accepted Answer

t = -ln(2)/k

Question 23

For A = A0 e^(kt) with k > 0, what is the doubling time?

Accepted Answer

t = ln(2)/k

Question 24

In a logistic growth model, what is the carrying capacity?

Accepted Answer

The limiting value of the output

Precalculus: Exponential and Logarithmic Functions flashcards

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