Chapter 4

4.4 – Exponential Equations & Applications

Warmup: Try this before checking the solution.
Solution: Try the warmup before checking the solution.

Objectives

Find exact solutions to equations with an unknown in an exponent.
Find approximate solutions to equations involving exponential & logarithmic functions using a graphing calculator.

Examples/Definitions

One way to solve an equation with an unknown expression in the exponent is to isolate the exponential term on one side of the equation and then take logarithms. After taking logarithms, the following properties may be used:

or for any expression x

or for any x, any u > 0 and any base a.

Exponential Growth and Decay

Many real world applications can be modeled by exponential growth or decay. When a quantity grows according to exponential growth it is said to grow exponentially. When a quantity decays according to exponential decay, it is said to decay exponentially.

Exponential Growth: where is the amount at t = 0 (the initial amount), k is the growth rate and Q is the amount at t units.

Exponential Decay: where is the amount at t = 0 (the initial amount), k is the decay rate and Q is the amount at t units.