(a) If you deposit $1 into a savings account that earns interest at an annual interest rate r (b) compounded n. times a year, then after one year, the initial deposit of $1 will have grown to an amount of dollars equal to Pn = (1+:)n 71 Use a computer or calculator to compute R, for n = 12, n = 52, and n = 365. To make it easier, let T = 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 innite amount of money in one year if you compound often enough? This is an experimental problem, so you just have to plug in larger and larger numbers for in until you convince yourself of an answer. If there is a maximum amount, write down what you think it is, accurate to at least 3 decimal places. Let f (m) = ex be the exponential function with the natural base 6. 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 h that are closer and closer to 0, estimate (using a computer or calculator) the slope of the line tangent to y = e'\" a the point where a: = 1. Write down the slope accurate to at least 3 decimal places