Day 2
GRAPHING EXPONENTIALS AND LOGS
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
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?
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?
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.
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.
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.
Graphing Exponential Decay
y = 24(1/3)x


Horizontal
Asymptote
Domain
x
-3
-2
-1
0

Range
1
2
3
y
Graphing Exponential Decay
y = 100(0.1)x
x

Horizontal asymptote

Domain

Range
-3
-2
-1
0
1
2
3
y
Graph and give asymptote, domain and range.
1 x
y  (2)
2
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)