Unit 6: Exponential and Logarithmic Functions

Front

What is an Exponential Function?

Back

A function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and b ≠ 1.

Front

What is Exponential Growth?

Back

A situation where a quantity increases at a rate proportional to its current value, typically modeled by f(x) = a * b^x with b > 1.

Front

What is Exponential Decay?

Back

A situation where a quantity decreases at a rate proportional to its current value, typically modeled by f(x) = a * b^x with 0 < b < 1.

Front

What is a Logarithm?

Back

The inverse operation to exponentiation, answering the question: to what exponent must a base be raised to produce a given number.

Front

What is the base of the common logarithm?

Back

10.

Front

How do you solve for x in an exponential equation?

Back

Set the exponents equal to each other if the bases are the same.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

What is the natural logarithm?

Back

The logarithm to the base e, denoted as ln(x), where e is approximately 2.718.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions can be converted to logarithmic form and vice versa; if y = b^x, then x = log_b(y).

Front

What is an asymptote in the context of exponential functions?

Back

A line that a graph approaches but never touches; for exponential decay, the horizontal asymptote is typically y = 0.