Exponential Functions Rate

L.15.2- Exponential Growth and Decay Functions



Essential Question: How can you use exponential functions to model the increase or decrease of a quantity over time?

Growth Function

The constant multiplier is bigger than 1. Meaning the starting value is keeping 100% of its value and adding some percent.

Decay Function

The constant multiplier is between 0 and 1. This number comes from subtracting the decay rate from 100% of the original starting value.

Growth and Decay in a Table

• If the constant multiplier is a number between 0 and 1 it is called a DECAY factor.

• (1 - decay rate) = decay factor.

• If the constant multiplier is bigger than 1 it is called a GROWTH factor.

• (1 + growth rate) = growth factor.

Steps for Exponential Problem Solving

1: Decide if the problem is describing exponential growth or decay. ("increase" = growth, "decrease" = decay)

2: Convert the growth or decay percentage to a decimal. This decimal is your r value. Ex: 23% = .23 and 5% = .05

3: Write your exponential equation. a is your starting value.

GROWTH: y = a(1 + r)^x

DECAY: y = a(1 - r)^x

4: Use the equation to solve the problem. Remember that x is input and y is output.