$1)$ You want to save up $$100,000$ and you find an broker advertising an account with $5\mathrm{.}5\%$ nominal interest compounded continuously.a$.$ What is the annual growth factor?b$.$ What is the APY $($aka annual percentage change$)?$c$.$ Suppose you invest P dollars in this account Write a function A$($t$)$ that gives the amount in the account after t years.d$.$ What is the $5-$year growth factor of this investment?e$.$ If you want to withdraw $$100,000$ in five years, how much should you initially invest in the account?f$.$ Set up an equation to find out how long it will take to have $$100,000$ dollars if you initially invest $$30,000.$ Solve via graphing$\mathrm{.}2)$ What is the better investment: an account with $5\mathrm{.}6\%$ APR compounded continuously, or an account with $5\mathrm{.}65\%$ APR compounded quarterly? Justify your answer with calculations.