1. 11.2 Exponential Functions

2. General Form Let a be a constant and let x be a variable. Then the general form of an exponential function is:

3. What does it mean? We talk about exponentials in 2 ways: Exponential Growth Exponential Decay

4. Growth In the equation below, when a > 1, we have exponential growth. Exponential growth is when something is growing without bound.

5. Decay In the equation below, when 0<a<1, we have exponential decay. This happens when something is decaying toward extinction.

6. Compounding Interest Compounding interest occurs when you earn interest on top of interest. An example would be a savings account. The following formula assumes that you are putting a lump sum into an account and not touching it for a number of years.

7. Compounding Interest Let A represent the amount of money in an account. Let P represent the principal investment. Let r represent the interest rate (APR) as a decimal. Let n represent the number of compounds per year. Let t represent the time in year. Then the formula for compounding interest is:

8. Compounding Interest Determine the future value of an account that has an initial investment of $3000 and is compounded quarterly at a rate of 6.5% for 20 years.

9. Compounding Interest

10. Annuity A series of payments made at equal intervals is known as an annuity. An example would be a retirement fund where a certain dollar amount is taken from each paycheck and put into an account. Notice this differs from the previous situation in that there are scheduled payments/contributions.

11. Present Value The present value of an annuity is the amount of money you currently have in the account. The following formula could be used to determine what the payment would be, for example, on a loan. Formula:

12. Example You take out a loan for a new car to the tune of $18,000. You land a cool 6.8% for 48 months. What will your monthly payment be?

13. Future Value The future value of an annuity is how much you can expect to have in the future assuming you make the scheduled contributions of a predetermined amount. You would use this formula to calculate, for example, the future value of a retirement fund. Formula:

14. Example You pledge to invest $180 per month into your child’s college savings plan. If the plan pays 4.6% APR, how much will it be worth in 18 years when they start college?

15. Pg. 612 # 17-25 [3], 41, 42 Homework