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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
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.
Graphing Exponential Equations
y = 2x
x y
-3
-2
-1
0
1
2
3
EXPONENTIAL GROWTH
y = a • bx time
initial amount growth factor (1+r)
Ex. The population of the US in 1994 was about 260
m...
Modeling growth
 The bear population increases at a rate
of 2% per year. There are 1573 bears this year.
Write a function...
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...
More Decay…..
The population of a certain animal species decreases at
a rate of 3.5% per year. You have counted 80
animals...
Ex: Analyzing a Function
Without graphing, determine whether the
function y = 14(0.95)x represents exponential
growth or e...
Graphing Exponential Decay
y = 24(1/3)x
 Horizontal
Asymptote
 Domain
 Range
x y
-3
-2
-1
0
1
2
3
Graphing Exponential Decay
y = 100(0.1)x
 Horizontal asymptote
 Domain
 Range
x y
-3
-2
-1
0
1
2
3
Graph and give asymptote, domain and range.
x
y )2(
2
1

Translating y = abx
y =8(1/2)x y = 8(1/2)x+2 +3
Translating y = abx
y =2(3)x-1 + 1 y = -3(4)x+1 +2
Homework
 Pg. 296 (1-14, 29-34)
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  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)

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