1. Sect 8.1 To model exponential growth and decay Section 8.2 To use e as a base and to apply the continuously and compounded interest formulas

2. EXPONENTIAL FUNCTIONS where ‘a’ is the beginning value or y-intercept ‘b’ is the base and ‘x’ is the exponent. Characteristics 1)Constant for a base (except 1). 2)Variable for an exponent. 3)Shows increasingly rapid growth when b > 1. 4)Shows increasingly rapid decay when the 0 < b < 1. 5)Horizontal Asymptote at y = 0.

3. Growth Functions Decay Functions

5. GRAPH OF THE NATURAL BASE ‘e’ FUNCTION ‘e’ is a constant, irrational number, much like π. The base ‘e’ occurs in many business, financial and engineering applications. ‘e’ ≈ 2.718…….. Graph: Horizontal asymptote is y = 0 xy 01 2 - 2

6. Ex 1. Ex. 2 Ex. 3

7. CONTINUOUS COMPOUND INTEREST This formula is used for continuous or an infinite number of compounds per year. A – Amount (after interest is earned) P – Principal (money initially invested) r – interest rate (percentage written as a decimal) t – time in years

8. * Ex. 1 Suppose you invest $1300 at an annual interest rate of 4.3% compounded continuously. Find the amount you will have in the account after 3 years. * Ex 2 Suppose you invest $100 at an annual interest rate of 4.8% compounded continuously. Find the amount you will have in the account after 3 years. * Ex 3 Suppose you put $1000 in an account earning 5.5% interest compounded continuously. How much will be in the account after one year? Four years?

9. COMPOUND INTEREST This formula is used for ‘n’ compounds per year where ‘n’ is a finite number. A – Amount (after interest is earned) P – Principal (money initially invested) r – interest rate (percentage written as a decimal) n – number of compounds per year t – time in years

10. COMPOUND INTEREST If $12,000 is invested into an account and it earns 9% interest, find the total amount in the account after 5 years if interest is compounded quarterly.

11. If $1,000 is invested into an account and it earns 8 ½ % interest, find the total amount in the account after 10 years if interest is compounded monthly. How much money would be in the account if interest were compounded continuously?

12. Suppose you would like to have $100,000 in an account 25 years from now. How much should you invest into an account that pays 12% interest and interest is compounded quarterly?