Applications of Exponential Functions

Today in class we learned about Applications of Exponential Functions.

There are three Formula's you should know

Formula for Growth and Decay

A=Pe^rt Where: A = Final amount, P = Initial amount, r = rate/constant, and t = time

Formula for Compound Interest

A=P(1+r/n)^rt Where: A - Final Amount, P = Inital Amount, r = Rate, n = number of compounds per year, and t = time.

Formula for Continuous Compound Interest

A=Pe^rt Where: A = Final amount, P = Initial amount, r = rate/constant, and t = time

Now that we know those questions lets do a couple questions.

Example 4 from the Exponents and Logarithms booklet.

A $15000 investment earns interest at the annual rate of 7.6% compounded quarterly.

Determine the value of the investment after 9 years

and the amount of interest earned after 9 years.

1. State what is given.

Initial amount = 15000

Rate = 7.6% = 0.076

time = 9 years

and n = 4

2. Plug in your values into your formula.

A= 15000(1+ 0.076/4)

A=15000(1.019)^36

The ^36 came from multiplying 9 by 4 since you are looking for the investment after 9 years and you are being compounded quarterly(4)

3.A= 29536.70

You have found out that the value of your investment is $29536.70 after 9 years. Now you want to find out the interest earned after 9 years.

4. Interest earned = Final Amount - Initial Amount

5. 29536.50 - 15000 = $14536.7

Example 2

Bacteria are growing according to y = A * 2^x. If the initial bacteria count is 10,000 determine how many hours it will take for the bacteria count to triple.

1. State what is given

A=10,000

final amount = 30000( since you know that the amount your looking for is tripled you mulitply your original initial amount which is 10,000)

time=x=?

The formula you would use would be A=Pe^rt

2. plug in your amounts

30000=10,000 * 2^x

divide both sides to get 2^x by it's self

3. 3=2^x

you can't make bases the same so you have to put logs in the front

4. log3 = log2^x

divide by log 2^x to get the x by it's self.

5. x= log3/log2

6. now you type in log3/log2 in you calculator and you should get 1.6 rounded off .

Thanks for reading and just a reminder that we have a test on Friday so start studying!