After discussing the graph, explain characteristics of exponential functions to the students.

Exponential Function: A function that involves the expression bx where the base b is a positive number other than 1

Asymptote: A line that a graph approaches as you move away from the origin

Exponential Growth Function: A function of the form f(x)=abx where a>0 and b>1

Growth Factor: The quantity 1+r in the exponential growth model y=a(1+r)t where a is the initial amount and r is the percent increase expressed as a decimal

Compound Interest: Consider an initial principal P deposited in an account that pays interest at an annual rate r, compounded n times per year. The amount A in the account after t years can be modeled by the equation

Exponential Decay Function: A function of the form f(x)=abx where a>0 and 0<b<1

Decay Factor: The quantity 1-r in the exponential growth model y=a(1-r)t where a is the initial amount and r is the percent decrease expressed as a decimal

Lesson Plan: Exponential Functions

Molly McKee

Use this question to introduce exponential growth.

Ask students to determine the solution before explaining exponential functions.

Ask questions to help guide students

•How many times did the rumor get told?

•How many people were told each time?

Discuss student solutions and their reasoning.

Figure A shows the graph of y=2x-1 as it passes through the origin.

Figure B shows how fast y=2x-1 grows.

Figure A

Figure B