Homework Questions!
Unit 3
Exploring Exponential Models
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
-3
-2
-1
0
1
2
3
y
EXPONENTIAL GROWTH
y = a • bx
initial amount
time
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
Ex. 1. 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…..
Ex. 2. 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.
An asymptote is a line that a graph
approaches as x or y increases in
absolute value.
Ex: Graphing Exponential Decay
y = 24(1/3)x
Identify.
x
• Horizontal
Asymptote
-3
-2
-1
• Domain
0
1
• Range
2
3
y
Example 5b Graphing Exponential Decay
y = 100(0.1)x
Identify.
•
Horizontal asymptote
•
Domain
•
Range
x
-3
-2
-1
0
1
2
3
y
Example 2 Translating y = abx
y =8(1/2)x
y = 8(1/2)x+2 +3
Example 2b Translating y = abx
y =2(3)x-1 + 1
y = -3(4)x+1 +2
Half-life!
What does that mean?
• The half-life is the amount of time it
takes for half of the atoms in a sample
to decay.
1 *t
A = A0(1/2) Half life
Example 3 Real World Connection
A hospital prepares a 100-mg supply of
technetium-99mg which has a half-life of 6
hours. Write an exponential function to find
the amount of technetium-99mg that remains
after 75 hours.
Another Half-Life?
• Arsenic-74 is used to locate brain
tumors. It has a half-life of 17.5 days.
Write an exponential decay function
for a 90-mg sample. Use the function
to find the amount remaining after 6
days.
Classwork/homework
• Worksheet