Take Note Key Concept: Exponential Growth and Decay

You can model exponential growth or decay with this function.

For growth or decay to be exponential, a quantity changes by a fixed percentage each time period.

Problem 3 Modeling Exponential Growth

You invested $1000 in a savings account at the end of 6th grade. The account pays 5% annual interest. How much money will be in the account after six years?

• Step 1 Determine if an exponential function is a reasonable model.

  The money grows at a fixed rate of 5% per year. An exponential model is appropriate.

• Step 2 Define the variables and determine the model.

  Let t = t equals  the number of years since the money was invested.

  Let A(t) = the amount in the account after each year.

  A reasonable model is A ( t ) = a ( 1 + r ) t . eh open t close equals eh . open 1 plus r close to the t . .

• Step 3 Use the model to solve the problem.

  A ( 6 ) = 1000 ( 1 + 0.05 ) 6 Substitute  a = 1000 , r = 0.05 , and  t = 6 .   = 1000 ( 1.05 ) 6 Simplify   ≈ $ 1340.10   table with 3 rows and 3 columns , row1 column 1 , eh open 6 close , column 2 equals , 1000 , open 1 plus , 0.05 , close to the sixth , column 3 cap substitute . eh equals , 1000 , comma r equals , 0.05 , comma , and , t equals 6 . , row2 column 1 , , column 2 equals , 1000 , open , 1.05 , close to the sixth , column 3 cap simplify , row3 column 1 , , column 2 almost equal to dollars , 1340.10 , column 3 , end table

  The account contains $1340.10 after six years.

✓ Got It?

3. Suppose you invest $500 in a savings account that pays 3.5% annual interest. How much will be in the account after five years?