1. GRAPH EXPONENTIAL DECAY FUNCTIONS
SECTION 7.2
GRAPH EXPONENTIAL DECAY FUNCTIONS

2. EXPONENTIAL GRAPHS Exponential Growth Exponential Decay
y = a•bx (b > 1)
y = 3(2)x
y = a•bx (0 < b < 1)
y = 3(0.5)x

3. Graph y = b for 0 < b < 1 x
EXAMPLE 1
Graph y = 1 2 x
SOLUTION
STEP 1
Make a table of values
STEP 2
Plot the points from the table.
STEP 3
Draw, from right to left, a smooth curve that begins just above the x-axis, passes through the plotted points, and moves up to the left.

4. Graph y = ab for 0 < b < 1 x
EXAMPLE 2
Graph the function.
a. Graph y = 2 1 4 x
SOLUTION
Plot (0, 2) and then ,
from right to left, draw a curve that begins just above the x-axis, passes through the two points, and moves up to the left. 1, 1 2 a.

5. EXPONENTIAL DECAY MODEL
y = a(1-r)t
Decay Factor: 1-r
a: initial amount
r: percent decrease as a decimal
t: time

6. EXAMPLE 4
Solve a multi-step problem
A new snowmobile costs $4200. The value of the snowmobile decreases by 10% each year.
Snowmobiles
• Write an exponential decay model giving the snowmobile’s value y (in dollars) after t years. Estimate the value after 3 years.
• Graph the model.
• Use the graph to estimate when the value of the snowmobile will be $2500.

7. EXAMPLE 4
Solve a multi-step problem
SOLUTION
STEP 1
The initial amount is a = 4200 and the percent decrease is r = So, the exponential decay model is:
y = a(1 – r) t
Write exponential decay model.
= 4200(1 – 0.10) t
Substitute 4200 for a and 0.10 for r.
= 4200(0.90) t
Simplify.
When t = 3, the snowmobile’s value is y = 4200(0.90)3 = $

8. The graph passes through the points (0, 4200) and (1, 3780).
EXAMPLE 4
Solve a multi-step problem
STEP 2
The graph passes through the points (0, 4200) and (1, 3780).
It has the t-axis as an asymptote. Plot a few other points. Then draw a smooth curve through the points.
STEP 3
Using the graph, you can estimate that the value of the snowmobile will be $2500 after about 5 years.