Question

Enter the exponential function using t (for time) as the independent variable to model the situation. Then find the value of the function after the given amount of time. A new savings account is opened with $200 and gains 3.1% yearly for 8 years. The exponential function that models the situation is . After 8 years, the savings account has $ . , , , and .

Answer 1

`(a)\ f(8) = 200(1 + 3.1\%)^8`

(b) After 8 years, the savings account has $255.32

Explanation:

Given

`a = 200` ---- initial (i.e. when t = 0)

`r =3.1\%`

`t = 8`

Solving (a): Model the situation

For growth, an exponential function is represented as:

`f(t) = a(1 + r)^t`

This gives:

`f(8) = 200(1 + 3.1\%)^8`

Solving (b): The solution to (a)

We have:

`f(8) = 200(1 + 3.1\%)^8`

Express percentage as decimal

`f(8) = 200(1 + 0.031)^8`

`f(8) = 200(1.031)^8`

`f(8) = 200*1.2766`

`f(8) = 255.32`