Unit 6: Exponential and Logarithmic Functions

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase.

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease.

The general form is f(x) = a * b^x, where a is the initial value, b is the growth (b > 1) or decay (0 < b < 1) factor.

The base of a logarithm is the number that is raised to a power to obtain a given number. For example, in log_b(a) = c, b is the base.

To convert from exponential form a^b = c to logarithmic form, use log_a(c) = b.

x = 3.

log_a(a) = 1, because a raised to the power of 1 equals a.

log_a(1) = 0, because a raised to the power of 0 equals 1.

5^2 = 25.

Exponential functions and logarithmic functions are inverses of each other.