Exponential and Logarithmic Functions Glossary

A line that a curve approaches but never reaches. Exponential functions have horizontal asymptotes; logarithmic functions have vertical asymptotes.

log_b(x) = log_c(x) / log_c(b), used to evaluate logarithms with non-standard bases using a calculator.

Logarithm with base 10. Often written as log(x) without a subscript.

Interest calculated on both the initial principal and previously earned interest: A = P(1 + r/n)^(nt).

Interest compounded infinitely often, modeled by A = Pe^(rt).

The set of all valid input values for a function. For logarithmic functions, the argument must be positive.

An irrational mathematical constant approximately equal to 2.71828, the base of the natural logarithm.

Decrease where the rate of decline is proportional to the current value, modeled by f(x) = a * b^x with 0 < b < 1.

A function of the form f(x) = a * b^x where b > 0 and b is not equal to 1.

Growth where the rate of increase is proportional to the current value, modeled by f(x) = a * b^x with b > 1.

The time required for a quantity undergoing exponential decay to reduce to half its initial value.

The inverse of exponentiation. log_b(x) = y means b^y = x.

Logarithm with base e, approximately 2.71828. Written as ln(x).