6. Exponential functions are useful in business and economics. Lesson 7 discusses them. Show how the values are entered into your functions and also calculate the amounts for each of the following:

b1. F = Pe^rt , which assumes continuous compounding, says that the Future value (F) of an amount (P) invested today at an annual rate (r), expressed as a decimal for the time (t), in years is given by the function (assuming continuous compounding). EXAMPLE: invest $100 at the annual rate of 5 1/2% for 6 years and 3 months and you should get back (at the end of the time), F = $100e^{(0.055)(6.25)} = $100e^(0.3438) = $100(1.4102) = $141.02. If you deposit $10000 today into your saving account, what amount would you have in 10 years if it can earn 6% per annum?

b2. Alternatively, P = F/e^rt. P tells you the most you should loan. EXAMPLE: A borrower tells you that he will give you back $141.02 at the end of a loan that for 6 years and 3 months with an interest rate of 5 1/2% per annum. The most you should have loaned him was P = $100. Here is a loan proposition more in line with current interest rates. A borrower agrees to pay