Given:
Amount of money A to which a principal investment P will grow after t years at interest rate r, compounded n times per year, is given by the formula,
![A=P(1+(r)/(n))^(nt)](https://img.qammunity.org/2023/formulas/mathematics/high-school/39foo2gerf9tf1ffk32zwshrn339mz02kv.png)
a) P= $4000, r=3% compounded daily.
The function A that models the amount to which the account grows after t years is,
![\begin{gathered} A=4000(1+(3)/(100(365)))^(365t) \\ A=4000(1+(0.03)/(365))^(365t) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/1mo835ik5h5v2pxloaezy17fa16uc8ll0c.png)
b) after 30 years the amount will be,
![\begin{gathered} A=4000(1+(0.03)/(365))^(365t) \\ A=4000(1+(0.03)/(365))^(365(30)) \\ A=4000(1.00008)^(10950) \\ A=9838.05 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/wss2eubbv4hte5orhma27ynw7ekxt3wacq.png)
Answer:
![A(30)=9838.05](https://img.qammunity.org/2023/formulas/mathematics/college/bsecbt1m54p70nvafcwwjl0ek20twr9482.png)