Ch 3.1 -3.2 Graded Flashcard (PC)

Front

What is compound interest?

Back

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Front

How do you calculate the amount in an account with compound interest?

Back

The formula is A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is an asymptote in mathematics?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

How do you find the asymptote of the function f(x) = 2^(x-1) + 3?

Back

The horizontal asymptote is y = 3.

Front

What is the definition of logarithm?

Back

A logarithm is the power to which a number must be raised to obtain another number. For example, log_b(a) = c means b^c = a.

Front

How do you solve the equation log_8(x) = 2?

Back

Convert to exponential form: x = 8^2 = 64.

Front

What is the change of base formula for logarithms?

Back

The change of base formula is log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.

Front

How do you convert logarithmic equations to exponential form?

Back

To convert log_y(x) = r to exponential form, write it as y^r = x.

Front

What is the value of log_10(100)?

Back

log_10(100) = 2, because 10^2 = 100.