Example $3.$ In business, the compound interest formula is A$=$ P$*(1+($I$/$M$))^($T$*$M$),$ where P is the principal $($present value or the original value of the investment$),$ I is the annual interest rate, M is the number of time the interest is computed per year, T is the number of years, and A is the value of the investment after T years.

a$.$ What type of function is this?

b$.$ What is the value of your investment after $5$ years, $10$years, $20$ years, $30,$ years, $40$ years and $50$ years if you deposit $$5000$ in an account that earns an $8\mathrm{.}5\%$ annual rate compounded quarterly?

Example $4.$ Windmills are increasingly being used to generate electricity. For moderate wind speeds, the power P in watts generated by a windmill us related to the wind speed v in miles per hour according to the equation