Let yt denote the amount of money in a bank account (in dollars) at time t. Suppose the bank is giving you 4 percent interest per year on your savings. Let the interest rate be denoted by i. Let y0 denote the amount of money in your bank account at time 0. Let y0 = 10 dollars.

(a) Write the expression for yt as a function of y0 and i. Show every step of all calculations.

(b) What is the amount of money in your bank account at time t = 8. Show every step of all

calculations.

(c) Use the Rule of 70 to compute how many years it will approximately take for the amount to

increase to 40 dollars.

(d) Calculate exactly how many years it will take for the amount to increase to 40 dollars.

part c) and part d). Why do they differ?

(e) Plot the bank balance on a standard scale when you let time t go from 0 to 50 on the horizontal axis.

(f) Make the same graph on a ratio scale.