How do you find out how much bacteria is growing on

your toothbrush?For example: if bacteria

grows by 25% each hour, how many will be on your

toothbrush in the morning?

In this lesson you will learn how to create and solve simple

exponential functionsby examining exponential

growth and decay problems

Let’s Review

Exponential growth/decay: Rate of growth is proportional to the current

value; this rate of growth is called the “growth factor” or “decay factor”

Let’s Review

40% growth 40% growth

Example: You start with 25 dots, and the number of dots increase by 40% in every step.

Let’s Review

y = a(1+r)x

y = 25(1+.4)x

y = 25(1.4)x

40% growth 40% growth

A Common Mistake

Growth Factor > 1 (example 1.4)

0 < Decay Factor < 1 (example 0.4)

Core Lesson

We will investigate the following:Bacteria are everywhere, including your

toothbrush! A colony of bacteria can grow by 25% every hour. If your toothbrush has a

starting colony of 5000 after you brush your teeth, how many bacteria will be on the

toothbrush in the morning, 8 hours later?

Core Lesson y = a(1+r)x

y = (5000)*(1+.25)xy = (5000)*1.25x

y = (5000)*1.258

5000 starting bacteria25% growth every hourhow many after 8 hours?

VERIFY: what does my answer mean? does this make sense?

y = 29,802

y ≈ 29,800 bacteria

In this lesson you have learned how to create and solve simple

exponential functionsby examining exponential

growth and decay problems

Guided Practice

When you buy a new car, its value quickly “depreciates”, or, loses its value. If a new car loses 15 percent of its value each year, and was originally purchased for $25000, what

will the car’s value be ten years after purchase?

Guided Practice y = abx

y = (25000)*bx

y = (25000)*.85x

y = (25000)*.8510

25000 starting value15% decay every yearhow much after 10 years?

VERIFY: what does my answer mean? does this make sense?

y = 4921

y ≈ $4900

Extension Activities

a. Bank accounts grow exponentially. Use the computer to look up some common “interest rates” and investigate how much money you could save in 5 years, 10 years, by the time you retire.

b. Investigate the depreciation value of your favorite car and evaluate whether you should buy new or used, and for how long you should own your favorite car.

Quick Quiz

1. Your bank account compounds (grows) by 5% each year at the end of the year. If you put $500 into your account, how much money will be in the account in 15 years?2. Polar bear populations have been on the decline in the Arctic recently. If the populations decreases by 10% each year, how many polar bears will remain in 25 years, with an initial population of 8000?