3.4 Using Exponents to Solve Problems February 26, 2013

Using Exponents to Solve Problems

Nathan Reading

http://flic.kr/p/beXKEz

When scientists study bacteria they must use some mathematical ideas about exponents to help them.

Bacteria are grown in the laboratory in gardens or cultures in small petri dishes.

By Nathan Reading http://flic.kr/p/9TtH1V

Salmonella species on X.L.D. agar.

3.4 Using Exponents to Solve Problems February 26, 2013

Bacteria grow through a process of cell division, where each cell divides itself into two more cells. Each of those cells divide into two more cells.

Bacterial growth keeps doubling, and is exponential. By counting the number of cells over a period of time, the scientists can learn about bacterial growth under certain conditions.

By AJC1http://flic.kr/p/M8mnY

The table below shows their observations:

Time Number of Bacteria

08:00 500

09:00 500 ∙ 2 = 1000

10:00 (500 ∙ 2) ∙ 2 = 2000

11:00 (500 ∙ 2 ∙ 2) ∙ 2 = 4000

12:00 (500 ∙ 2 ∙ 2 ∙ 2) ∙ 2 = 8000

By AJC1http://flic.kr/p/M8mnY

3.4 Using Exponents to Solve Problems February 26, 2013

After 24 hours of growth at this rate, the bacterial count will reach:

What's the problem with this?

By AJC1http://flic.kr/p/M8mnY

We can write this as an exponent:

By AJC1http://flic.kr/p/M8mnY

3.4 Using Exponents to Solve Problems February 26, 2013

Example 1

A patch of algae on the surface of a pond triples in size each month. It took 6 months for the algae to cover the pond. How long did it take for the algae to cover half of the pond?

Example 2

If the starting population of 100 mosquitoes doubles each week, how many mosquitoes will there be in:

a.) 4 weeks? b.) 3 months? (Hint: 1/4 of 52 weeks)

3.4 Using Exponents to Solve Problems February 26, 2013

Extension : Example 3

A rubber ball was dropped from the top of a building. Each time it hit the ground, it bounced back to a height equal to half of the height from which it fell. The ball was dropped from a height of 32 feet. How high does the ball bounce after the 5th bounce?

Assignment

1.) If the starting population of 5 rabbits doubles each year, how many rabbits will there be in:

a.) 20 years? b.) 50 years?

2.) A population of 100 frogs triples yearly. How many frogs will there be ina.) 5 years? b.) 10 years?c.) 50 years?

3.) A species of extremely rare, deep water fish has an extremely rarely have children. If there are 821 of this type of fish and they double each year, how many will there be in a.) half of a year?b.) 10 yearsc.) 100 years?

Extension4.) A type of medication once taken has an exponential decay rate of 1/5 every hour. If there are 10 mg in a dose, determine how many mgs are in the body in

a.) 5 hours?b.) 1 day?

3.4 Using Exponents to Solve Problems February 26, 2013