4­1 Exponential Functions, Growth and Decay­ period 1.notebook
January 13, 2015
Bellwork 1-13-15
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4­1 Exponential Functions, Growth and Decay­ period 1.notebook
January 13, 2015
You can model growth or decay by a constant percent increase or
decrease with the following formula:
In the formula, the base of the exponential expression, 1 + r, is
called the growth factor. Similarly, 1 – r is the decay factor.
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4­1 Exponential Functions, Growth and Decay­ period 1.notebook
January 13, 2015
Helpful Hint
X is used on the graphing calculator for the variable t:
Y1 =5000*1.0625^X
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4­1 Exponential Functions, Growth and Decay­ period 1.notebook
January 13, 2015
Example 2: Economics Application
Clara invests $5000 in an account that pays 6.25% interest per
year. After how many years will her investment be worth
$10,000?
Step 1
Write a function to model the growth in value of her investment.
f(t) = a(1 + r)t
Exponential growth function.
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4­1 Exponential Functions, Growth and Decay­ period 1.notebook
January 13, 2015
Example 2 Continued
Step 2 When graphing exponential functions in an appropriate domain,
you may need to adjust the range a few times to show the key points of
the function.
Step 3 Use the graph to predict when the value
of the investment will reach $10,000. Use the
feature to find the t-value where f(t) ≈ 10,000.
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4­1 Exponential Functions, Growth and Decay­ period 1.notebook
January 13, 2015
Example 2 Continued
Step 3 Use the graph to predict when the
value of the investment will reach $10,000.
Use the
feature to find the t-value
where f(t) ≈ 10,000.
The function value is approximately 10,000 when t ≈ 11.43 The investment will be
worth $10,000 about 11.43 years after it was purchased.
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4­1 Exponential Functions, Growth and Decay­ period 1.notebook
January 13, 2015
Example 3: Depreciation Application
A city population, which was initially 15,500, has been dropping
3% a year. Write an exponential function and graph the
function. Use the graph to predict when the population will drop
below 8000.
f(t) = a(1 – r)t
Exponential decay function.
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4­1 Exponential Functions, Growth and Decay­ period 1.notebook
January 13, 2015
Example 3 Continued
10,000
Graph the function. Use
to
find when the population will fall
below 8000.
0
0
150
It will take about 22 years for the population to fall below 8000.
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4­1 Exponential Functions, Growth and Decay­ period 1.notebook
January 13, 2015
Lesson Quiz
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. Use a graph to 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. Use a graph to predict the value in 4 years.
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4­1 Exponential Functions, Growth and Decay­ period 1.notebook
January 13, 2015
Homework: Workbook Page 195 and 198
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