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# Day 2 worked

Graphing

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### Day 2 worked

1. 1. G R A P H I N G E X P O N E N T I A L S A N D L O G S Day 2
2. 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. 3. Graphing Exponential Equations y = 2x x y -3 -2 -1 0 1 2 3
4. 4. 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. 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. 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. 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. 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. 9. Graphing Exponential Decay y = 24(1/3)x  Horizontal Asymptote  Domain  Range x y -3 -2 -1 0 1 2 3
10. 10. Graphing Exponential Decay y = 100(0.1)x  Horizontal asymptote  Domain  Range x y -3 -2 -1 0 1 2 3
11. 11. Graph and give asymptote, domain and range. x y )2( 2 1 
12. 12. Translating y = abx y =8(1/2)x y = 8(1/2)x+2 +3
13. 13. Translating y = abx y =2(3)x-1 + 1 y = -3(4)x+1 +2
14. 14. Homework  Pg. 296 (1-14, 29-34)