Question

On the day of your birth, your parents open a college savings account with an initialinvestment of $3500. The account pays interest at a rate of 4% compounded yearly.a) Write an exponential function of the form given in the picture that models the accountbalance over timeb) Use the function to find the account balance after 18 years.

Answer 1

Given

initial investment of $3500

Rate = 4%

Find

a) Write an exponential function

b) Find the account balance after 18 years

Step-by-step explanation

as we know the exponential function is in the form of

`y=A(1+r)^t`

here , we have given , A = $3500 , r = 4%

so ,

`\begin{gathered} y=3500(1+(4)/(100))^t \\ \\ y=3500(1.04)^t \\ \end{gathered}`

b) account balance after 18 years =

`\begin{gathered} y=3500(1.04)^(18) \\ \\ y=3500*(1.04*1.04*1.04*1.04*.......18\text{ times\rparen} \\ \\ y=3500*2.02582(approx) \\ \\ y=7090.3578038 \end{gathered}`

Final Answer

therefore ,

a) Exponential function is

`y=3500(1.04)^t`

b) amount balance = $7090.36