Page 68 - Math Course 3 (Book 1)

Exponential Functions

MO. 2 - L5b What is the value of the car after five years?

Identifying Exponential V = 25,000 • 0.82 t 5 Original equation
Behavior V = 25,000 • 0.82 t = 5
V = 9268.50

Use a calculator.
Let’s Begin Answer After five years, the car’s value is
about $9,270.

Identify Exponential Behavior
Use Exponential Functions to Solve Problems

Example Example

Determine whether the set of data displays
exponential behavior. Explain why or why not.
DEPRECIATION
Some people say that the value of a new car
decreases as soon as it is driven off the dealer’s x 0 10 20 30
t
lot. The function V = 25,000 • 0.82 models the
depreciation of the value of a new car that originally y 10 25 62.5 156.25
cost $25,000. V represents the value of the car and
t represents the time in years from the time the car
was purchased. Method 1 Look for a Pattern

Graph the function. The domain values are at regular intervals of
10. Look for a common factor among the range
What values of V and t are meaningful in the values.
function?
10 25 62.5 156.25
Use a graphing calculator to graph the function.
× 2.5 × 2.5 × 2.5

Answer
Since the domain values are at regular intervals
and the range values have a common factor, the
data are probably exponential. The equation for
the data may involve (2.5)x.

Method 2 Graph the Data

[0, 15] scl: 1 by [0, 25000] scl: 5000

Only the values of 0 ≤ V ≤ 25,000
Answer and t ≥ 0 are meaningful in the
context of the problem.

What is the value of the car after one year?

t
V = 25,000 • 0.82 Original equation
1
V = 25,000 • 0.82 t = 1
V = 20,500 Use a calculator.
After one year, the car’s value is The graph shows a rapidly increasing value of y
Answer as x increases. This is a characteristic of
about $20,500.
exponential behavior.
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