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:

a1. You learn on the business channel that inflation was about 0.3% last month.Assume this rate is maintained each month for a year.What will the annualized rate be?EXAMPLE:A rate of 0.1% per month represents (1 + 0.001)¹²-1 = 0.0121 or 1.21% annually.

a2.You are trying to manage expenses, and decide that you will allow them to grow only 7% this year.Assuming you want a level (the same) monthly growth rate for each month, what will be the monthly growth rate that the 7% annual rate allows?EXAMPLE: A 2% growth rate for the year would require 1.02 = (1 + r)¹².Solve this for r:; r = .00165 or .165% per month on average.

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.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.Here is a CD offer more in line with current rates.You have $5500 to invest.The bank will pay you 0.45% per annum.If you place your money for 1 year 6 months in this CD, what do you expect to get back at the end of the period?

b2.Alternatively, P = F/e^rt.P tells you the most you should loan or the most you need now to save to meet future goal F.Thus, if a borrower tells you that he needs a loan for 6 years and 3 months and will pay you an annual rate of 5 1/2% for the loan, but will give you only $141.02 back at the end of the loan term, youshouldonly loan him $100 today.In 6 years you plan to spend $35500 on a new car.Assuming you can earn 3 1/2% annually on your savings, what amount do you need to save today to meet your goal 6 years hence?

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: al. You learn on the business channel that inflation was about 0.3% last month. Assume this rate is maintained each month for a year. What will the annualized rate be? EXAMPLE: A rate of 0.1% per month represents (1 + 0.001)12 -1 = 0.0121 or 1.21% annually. a2. You are trying to manage expenses, and decide that you will allow them to grow only 7% this year. Assuming you want a level (the same) monthly growth rate for each month, what will be the monthly growth rate that the 7% annual rate allows? EXAMPLE: A 2% growth rate for the year would require 1.02 = (1 + r)12. Solve this for : r = '71.02-1; r= 00165 or .165% per month on average. b1. F= Pert 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. 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. Here is a CD offer more in line with current rates. You have $5500 to invest. The bank will pay you 0.45% per annum. If you place your money for 1 year 6 months in this CD, what do you expect to get back at the end of the period? b2. Alternatively, P = F/ent. P tells you the most you should loan or the most you need now to save to meet future goal F. Thus, if a borrower tells you that he needs a loan for 6 years and 3 months and will pay you an annual rate of 5 1/2% for the loan, but will give you only $141.02 back at the end of the loan term, you should only loan him $100 today. In 6 years you plan to spend $35500 on a new car. Assuming you can earn 3 1/2% annually on your savings, what amount do you need to save today to meet your goal 6 years hence