Slide 1exponential function
base asymptote
model growth and decay situations.
Objective
Notes
In 2000, the world population was 6.08 billion and was increasing at a rate 1.21% each year.
1. Write a function for world population. Does the function represent growth or decay?
2. Predict the population in 2020.
The value of a $3000 computer decreases about 30% each year.
3. Write a function for the computer’s value. Does the function represent growth or decay?
4. Predict the value in 4 years.
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Exponential Functions, Growth, and Decay
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Exponential Functions, Growth, and Decay
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Exponential Functions, Growth, and Decay
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Exponential Functions, Growth, and Decay
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Negative exponents indicate a reciprocal. For example:
Remember!
In the function y = bx, y is a function of x because the value of y depends on the value of x.
Remember!
Tell whether the function shows growth or decay. Then graph.
Example 1A: Graphing Exponential Functions
Step 1 Find the value of the base.
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Example 1A Continued
Step 2 Graph the function by using a table of values.
x
0
2
4
6
8
10
12
f(x)
10
5.6
3.2
1.8
1.0
0.6
0.3
Tell whether the function shows growth or decay. Then graph.
Example 1B: Graphing Exponential Functions
Step 1 Find the value of the base.
g(x) = 100(1.05)x
The base, 1.05, is greater than 1. This is an exponential growth function.
g(x) = 100(1.05)x
Exponential Functions, Growth, and Decay
Tell whether the function p(x) = 5(1.2x) shows growth or decay. Then graph.
Step 1 Find the value of the base.
Example 1C
p(x) = 5(1.2 x)
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Exponential Functions, Growth, and Decay
Step 2 Graph the function by using a table of values.
Example 1C Continued
Exponential Functions, Growth, and Decay
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Exponential Functions, Growth, and Decay
Clara invests $5000 in an account that pays 6.25% interest per year. What will her investment be worth in seven years?
Example 2A: Economics Application
Step 1 Write a function to model the growth in value of her investment.
f(t) = a(1 + r)t
Exponential growth function.
f(t) = 5000(1 + 0.0625)t
Exponential Functions, Growth, and Decay
Clara invests $5000 in an account that pays 6.25% interest per year. What will her investment be worth in seven years?
Example 2A: Economics Application
f(t) = 5000(1.0625)t
Exponential Functions, Growth, and Decay
In 1981, the Australian humpback whale population was 350 and increased at a rate of 14% each year since then. Write a function to model population growth.
P(t) = a(1 + r)t
P(t) = 350(1 + 0.14)t
Exponential Functions, Growth, and Decay
A city population, which was initially 15,500, has been dropping 3% a year. Write an exponential function. What will the population be after ten years?
Example 3: Depreciation Application
f(t) = 15,500(1 – 0.03)t
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Notes
In 2000, the world population was 6.08 billion and was increasing at a rate 1.21% each year.
1. Write a function for world population. Does the function represent growth or decay?
P(t) = 6.08(1.0121)t
2. Use a graph to predict the population in 2020.
≈ 7.73 billion
The value of a $3000 computer decreases about 30% each year.
3. Write a function for the computer’s value. Does the function represent growth or decay?
4. Use a graph to predict the value in 4 years.
V(t)≈ 3000(0.7)t
Exponential Functions, Growth, and Decay
5. Tell whether the function shows growth or decay. Then graph.
Notes (continued)
f(x) = 8(½)x