How do you find out how much bacteria is growing on your toothbrush?

1. 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?

2. In this lesson you will learn how to create and solve simple exponential functions by examining exponential growth and decay problems

3. Exponential growth/decay: Rate of growth is proportional to the current value; this rate of growth is called the “growth factor” or “decay factor”

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

5. y = a(1+r)x y = 25(1+.4)x 40% growth 40% growth y = 25(1.4)x

6. Growth Factor > 1 (example 1.4) 0 < Decay Factor < 1 (example 0.4)

7. 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?

8. y = a(1+r)x y = (5000)*(1+.25)x 5000 starting bacteria y = (5000)*1.25x 25% growth every hour y = (5000)*1.258 how many after 8 hours? y = 29,802 y ≈ 29,800 bacteria VERIFY: what does my answer mean? does this make sense?

9. In this lesson you have learned how to create and solve simple exponential functions by examining exponential growth and decay problems

10. 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?

11. y = abx y = (25000)*bx 25000 starting value y = (25000)*.85x 15% decay every year y = (25000)*.8510 how much after 10 years? y = 4921 y≈ $4900 VERIFY: what does my answer mean? does this make sense?

12. 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. • 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.

13. 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?