Respuesta :
Answer:
D. [tex]f(t)=3500(1.035)^t[/tex]
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: [tex]y=a*b^x[/tex], 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.
[tex]3.5\%=\frac{3.5}{100}=0.035[/tex]
Upon substituting our given values in exponential function formula we will get,
[tex]f(t)=3500(1+0.035)^t[/tex]
[tex]f(t)=3500(1.035)^t[/tex], where, f(t) represents total balance in the account after t years.
Therefore, the function [tex]f(t)=3500(1.035)^t[/tex] represents the balance of the account after t years and option D is the correct choice.
