Exponential growth & decay

This course is a part of Mathematics II, a 14-course Topic series from Khan Academy.

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

This course contains 6 segments:

Equivalent forms of exponential expressions

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

Exponential equations: properties of exponents

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.

Interpreting the rate of change of exponential models

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

Constructing exponential models according to 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.

Advanced interpretation of exponential models

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.

Distinguishing between linear and exponential growth

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