Understanding Exponential Functions and Graphing

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

Exponential function A function in the form of y = ? ?? Examples:

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)

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

Evaluate the function for the given value. ? = 3 4? for x = 3 ? = 3 4( ) 3 ? = 3 64 ? = 192

What is the graph of y = 3 2?? Does the graph represent growth or decay? growth y = 3 2? (x, y) x 10 9 y = 3 2 2 (-2, 3 -2 4) 8 7 c c 6 y = 3 2 1 (-1, 1 1 -1 2) 5 4 y = 3 20 0 3 (0, 3) 2 1 1 y = 3 21 0 (1, 6) -1 -2 y = 3 22 2 (2, 12) -5 -4 -3 -2 -1 0 1 2 3 4 5

Does the table or rule represent a linear or an exponential function? A. ANSWER: EXPONENTIAL FUNCTION. x y B. y = 3x 0 0 1 3 ANSWER: LINEAR FUNCTION. 2 6 3 9

Pg 457: 8-17, 20,21

Suppose 30 flour beetles are left undisturbed in a warehouse bin. The beetle population doubles each week. The function f(x) = 30 2? gives the population after x weeks. How many beetles will there be after 56 days? 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) = 30 2? gives the population after x weeks. How many beetles f(x) = 30 2? What does x represent? = 30 28 = 30 256 = 7680 Answer: after 56 days, there will be 7,680 flour beetles.

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 ? = 360 1.0713 ? = 867.5442001 ? = $867.5 billion ?? $868 ???????

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) ? = 101 .8853 ? = 70.0085 ? = 70 kilopascals

When a bank pays interest on both the principal and the interest an account has earned. (it uses the following formula) r = the annual interest rate--- -convert from % to a decimal (move 2 places to the left) Compound interest: A = The balance r n)nt t= the time in years A = P( 1 + P = the principal (the initial deposit) n = the number of times interest is compounded per year

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

Find the balance in the account after the given period: $20,000 principal earning 3.5% compounded monthly, after 10 years 20,000 .035 12 10 P = r = n = t = r n)nt A = P( 1 + A = 20,000( 1 +.035 12)12(10) A = $28,366.90

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