Section 7.7- Exponential Growth and Decay
Essential Question: How can we model something that grows or decays at an extremely
fast rate?
Do Now:
You have just won a cash prize from a game show! The host tells you that you have
three choices you can pick from. The three options are:
Part 1
Prize #1: You get $100 right now plus $2 every day for a week.
Prize #2: You get $2 right now plus $100 every day for a week.
Prize #3: You get $5 right now and the money doubles every day for a week.
Which prize would you choose? Why?
Part 2
Match the equation with the corresponding prize in part 1. Let x=number of days.
1.
Equation
𝑦 = 5 ∙ 2𝑥
2.
𝑦 = 100 + 2𝑥
3.
𝑦 = 2 + 100𝑥
Which Corresponding Prize
Part 3
How much money do you get at the end of the week with each prize?
Prize 1
Prize 2
Prize 3
Part 4
Assume the prize is changed to a month. Would you keep the same prize of switch your
choice?
Exponential Functions
Exponential Growth

General Equation: _________________
Exponential Decay
Values for a and b:
o __________________
Sample Graph

Values for a and b:
o __________________
Sample Graph
Example 1: Modeling Exponential Growth
Suppose that in 1985, there were 285 cell phone subscribers in a small town. The
number of subscribers increased by 75% each year after 1985. How many cell phone
subscribers were in the small town in 1994? Write an expression to represent the
equivalent monthly cell phone subscription increase.
HINT: Use the general equation with exponential functions to help you model this
situation.
Compound Interest Formula
𝑟 𝑛𝑡
𝐴 = 𝑃 (1 + )
𝑛
Example 2: Compound Interest
Suppose that when your friend was born, your friend’s parents deposited $2000 in an
account that pays 2.5% interest compounded monthly. What will the account balance be
after 18 years?
Example 3: Modeling Exponential Decay
Example 4: Using Exponential Functions to Solve Equations
A fisheries manager determines that there are approximately 3000 bass in a
lake.
a. The population is growing at a rate of 2% per year. The function that models
that growth is y = 3000 • 1.02x. How many bass will live in the lake after 4
years?
b. How many bass will live in the lake after 7 years?
c. About how long will it be before there are 4000 bass in the lake?
Classwork:
7.7 Practice Form K (Odds only)
HW:
p. 464-465 #9-17 odds, 23-27 odds, 28-30, 34