7-6 & 7-7 Exponential Functions

1. 7-6 & 7-7 Exponential Functions Evaluate and graph exponential functions

2. Exponential function A function in the form of y = Examples:

3. Exponential Growth, modeled by the following y = a Initial amount (this is when x = 0) exponent The base & when b>1, called the Growth factor (1 + the percent rate written as a decimal)

4. Exponential Decay Initial amount (this is when x = 0) exponent The base is the decay factor (1 minus percent rate written as a decimal)

5. Evaluate the function for the given value. for x = 3

6. What is the graph of y = ? Does the graph represent growth or decay? growth y = (-2, ) y = (-1, 1 ) cc y = (0, 3) y = (1, 6) y = (2, 12)

7. Does the table or rule represent a linear or an exponential function? A. EXPONENTIAL FUNCTION. ANSWER: B. y = 3x ANSWER: LINEAR FUNCTION.

8. Pg 457: 8-17, 20,21

9. Suppose 30 flour beetles are left undisturbed in a warehouse bin. The beetle population doubles each week. The function f(x) = gives the population after x weeks. How many beetles will there be after 56 days? Suppose 30 flour beetles are left undisturbed in a warehouse bin. The beetle population doubles each week. The function f(x) = gives the population after x weeks. How many beetles will there be after 56 days? f(x) = What does x represent? = = = Answer: after 56 days, there will be 7,680 flour beetles.

10. Since 2005, the amount of money spent at restaurants in the US has increased about 7% each year. In 2005, about $360 billion was spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2018? Let y = The annual amount spent in restaurants (in billions of dollars) Let a = The initial amount: 360 Let b = The growth factor: (1 + %) or 1 + .07 = 1.07 Let x = The number of years since 2005: 13

11. The kilopascal is a unit of measure for atmospheric pressure. The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure decreases about 11.5%. What is the approximate pressure at an altitude of 3000 m? Let y = The atmospheric pressure (in kilopascals) Let a = The initial amount: 101 Let b = The decay factor: (1 - %) or 1 - .115 = .885 3 Let x = The altitude (in thousands of meters)

12. When a bank pays interest on both the principal and the interest an account has earned. (it uses the following formula) Compound interest: r = the annual interest rate----convert from % to a decimal—(move 2 places to the left) A = The balance t= the time in years P = the principal (the initial deposit) n = the number of times interest is compounded per year

13. Find the balance in the account after the given period: $12,000 principal earning 4.8% compounded annually, after 7 years 12,000 P = r= n= t = .048 1 7 A = $16,661.35

14. Find the balance in the account after the given period: $20,000 principal earning 3.5% compounded monthly, after 10 years 20,000 P = r= n= t = .035 12 10 A = $28,366.90

15. Pg 457: 18,19 pg 464: 9-21 odd (skip 13) Pg 457: 18,19 pg 464: 9,15,17,19,21