Question

Franklin deposits $3500 in an account that earns 3.5% interest compounded annually.Which function equation represents the balance of the account after t years? f(t)=3500(3.5)tf(t)=3500(1.35)tf(t)=3500(0.035)tf(t)=3500(1.035)t

Answer 1

f(t)=3500(1.035)t

Answer 2

D.
`f(t)=3500(1.035)^t`

Step-by-step explanation:

We have been given that Franklin deposits $3500 in an account that earns 3.5% interest compounded annually.

Since amount is increasing exponentially, so we will use exponential function to write the formula for our function.

Since an exponential function is in form:
`y=a*b^x`, where,

a = Initial amount,

b = For growth b is in form (1+r), where r represents growth rate in decimal form.

Let us convert our given rate in decimal form.

`3.5\%=(3.5)/(100)=0.035`

Upon substituting our given values in exponential function formula we will get,

`f(t)=3500(1+0.035)^t`

`f(t)=3500(1.035)^t`, where, f(t) represents total balance in the account after t years.

Therefore, the function
`f(t)=3500(1.035)^t` represents the balance of the account after t years and option D is the correct choice.