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Graphing Exponentials and Logs

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1 Graphing Exponentials and Logs
Day 2 Graphing Exponentials and Logs

2 An exponential function is a function with the general form of:
y = abx where x is a real number, a ≠ 0, b > 0, and b ≠ 1.

3 Graphing Exponential Equations
y = 2x x y -3 -2 -1 1 2 3

4 initial amount growth factor (1+r)
EXPONENTIAL GROWTH y = a • bx time initial amount growth factor (1+r) Ex. The population of the US in 1994 was about 260 million with an average annual rate of increase of about 0.7%. 1. Write a function to model this population. 2. What was the population in 2006?

5 Modeling growth The bear population increases at a rate
of 2% per year. There are 1573 bears this year. Write a function that models the bear population. How many bears will there be in 10 years?

6 Exponential Decay: y = a(1-r)t
Suppose you want to buy a used car that costs $11,800. The expected depreciation of the car is 20% per year. Estimate the depreciated value of the car after 6 years.

7 More Decay….. The population of a certain animal species decreases at a rate of 3.5% per year. You have counted 80 animals in the habitat. Write the equation.

8 Ex: Analyzing a Function
Without graphing, determine whether the function y = 14(0.95)x represents exponential growth or exponential decay. Without graphing, determine whether the function y = 0.2(5)x represents exponential growth or exponential decay.

9 Graphing Exponential Decay
y = 24(1/3)x Horizontal Asymptote Domain Range x y -3 -2 -1 1 2 3

10 Graphing Exponential Decay
y = 100(0.1)x Horizontal asymptote Domain Range x y -3 -2 -1 1 2 3

11 Graph and give asymptote, domain and range.

12 Translating y = abx y =8(1/2)x y = 8(1/2)x+2 +3

13 Translating y = abx y =2(3)x-1 + 1 y = -3(4)x+1 +2

14 Homework Pg. 296 (1-14, 29-34)


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