Since, it is an exponential function, thus this is a compound interest problem;
Where; the function is given as;
[tex]\begin{gathered} A(t)=P(1+r)^t \\ \text{Where A(t)= amount in the savings account at a time t} \\ P=ca\text{ pital invested} \\ r=\text{rate } \\ t=\text{ time} \end{gathered}[/tex]
Thus, the function required is;
[tex]\begin{gathered} A(t)=400(1+\frac{3.5}{100})^t \\ A(t)=400(1.035)^t \end{gathered}[/tex][tex]\begin{gathered} y=400(1.035)^t \\ \text{Where t is the time} \end{gathered}[/tex]
After 5 years,
[tex]\begin{gathered} A(5)=400(1.035)^5 \\ A(5)=400(1.1877) \\ A(5)=475.07 \end{gathered}[/tex]
The amount in the savings account after five years is $475.07
