# Exponential growth and decay

Contents

Learn how to analyze and manipulate exponential functions and expressions in order to study their rate of change.

Learn how to manipulate exponential expressions in different ways. For example, rewrite 8^x as 2^(3x).

Learn how to solve advanced exponential equations by manipulating the expressions in the equations using the properties of exponents. For example, solve 2^(x+1)=8^x by rewriting 8^x as 2^(3x) and then equating x+1=3x.

Learn about different ways of describing the rate of change of exponential functions.

Learn how to analyze exponential modeling functions in order to find their rate of change.

Learn how to find the modeling function of an exponential real world context, according to the description of its rate of change.

Learn how to interpret an exponential modeling function by first manipulating it according to your needs. For example, rewrite 5^(2x+1) as 5*25^x to find that the unit growth factor is 25.

Learn how to analyze real-world quantitative relationships given as tables of values to determine whether they represent linear growth or exponential growth.