Suppose that $$87,000$ is invested at $3\frac{1}{2}\%$ interest, compounded quarterly.

a$)$ Find the function for the amount to which the investment grows after $\mathrm{????}$ years.

b$)$ Find the amount of money in the account at $\mathrm{????}=0,3,8,$ and $10$ years.

a$)$ The function for the amount to which the investment grows after $\mathrm{????}$ years is $\mathrm{????}(\mathrm{????})=($Simplify your answer. Type an expression using t as the variable.$)$

b$)$ Find the amount of money in the account at $\mathrm{????}=0,3,8,$ and $10$ years.