(a) (b) If you deposit $1 into a savings accolmt that earns interest at an annual interest rate \"r compounded n times a year, then after one year, the initial deposit of $1 will have grown to an amount of dollars equal to P\": (1+:)n '. Use a computer or calculator to compute PR for n = 12, n = 52, and n = 365. To make it easier, let 7' = 1, which means the bank is giving you a 100% annual interest rate! (How generous of them!) What do these choices for 'n. represent in terms of the calendar? Is there an upper bound to how much you can make by compounding interest more frequently? Or will you eventually make an infinite amount of money in one year if you compmmd often enough? This is an experimental problem, so you just have to plug in larger and larger numbers for n lmtil you convince yourself of an answer. If there is a maximlnn amount, write down what you think it is, accurate to at least 3 decimal places. Let f (11:) : c:E be the exponential function with the natural base (3. Write down a formula for the slope of the secant line passing through the points (1, f(1)) and (1 + h, f (1 + h)). By choosing values for it that are closer and closer to 0, estimate (using a computer or calculator) the slope of the line tangent to y 2 :3I a the point where :r: = 1. Write down the slope accurate to at least 3 decimal places