8-5 Write Exponential Growth Models

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8-5 Write Exponential Growth Models

• Homework
• 524/4-7 10-20 even 22-32 even 38-39 52-60 even

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Exponential Function
y 3(2)x

• An equation in two variables that can be written
  in the form y abx
• a is not equal to 0.
• b gt 0
• b is not equal to 1.
• Exponential Growth
• a gt 0
• b gt 1

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Compare the data tables.
y 3x
As x increases by 1, each y value is added by 3
x -2 -1 0 1 2
y -6 -3 0 3 6
This is a linear function.
y 3x
As x increases by 1, each y value is multiplied
by 3
x -2 -1 0 1 2
y 1/9 1/3 1 3 9
This is an exponential function.
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Write a rule for the function.

• Analyze how the variables are changing.
  
• x increases by one each time.
• y is multiplied by 5 each time
  exponential y abx
• This means the base is 5 b 5.

• Find a by finding the value of y when x 0.

• y ab x
• 10 a5o
• 10 a 1
• a10
• Write the function rule.
• y 10 5x

y 10(5x)
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Write a rule for the function.
y abx

• x increases by one each time.
• y is multiplied by 3 each time.
• This means the base is 3 b 3.
• Find a by finding the value of y when x 0.
• When x is zero, y 9.
• Substitute 9 for a.
• a9
• Write the function rule.
• y 9 3x

y 9(3x)
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Write a rule for the function.
y abx
y abx
y 1(3x )
y 1(5x )
y 3x
y 5x
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Write a rule for the function.
y abx
y abx
y 1(11x )
y ½ (2x )
y 11x
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Write a rule for the function.
y abx
y abx
y -1(4x )
y 5 (2x )
y -4x
9
Solve a compound interest problem.
Investment You put 250 in a savings account
that earns 4 annual interest compounded yearly.
You do not make any deposits or withdrawals. How
much will your investment be worth in 10 years?
When a quantity grows exponentially, it increases
by the same percent over equal time periods.
EXPONENTIAL GROWTH MODEL y a(l r)t
a is the initial amount. r is the growth
rate. (1 r) is the growth factor. t is the time
period.
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Solve a compound interest problem.
Investment You put 250 in a savings account
that earns 4 annual interest compounded yearly.
You do not make any deposits or withdrawals. How
much will your investment be worth in 10 years?
y a(l r)t
initial amount growth rate growth
factor time period
250.you put 250 in a savings account
0.04.that earns 4 annual interest
(1.04) (10.04)
10.be worth in 10 years
y 250(l.04)10
Your savings account will be worth 370.06 in 10
years.
y 370.06
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This is the key you use to raise the base to a
power. Practice on your calculator. Your key
entry for the previous problem is
this 250(1.04)10
The parentheses are very important!
Always ask yourself if your answer makes sense
for the situation in the word problem.
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growth rate growth factor Initial amount
growth rate growth factor Initial amount
growth rate growth factor Initial amount
0.75
0.05
0.25
1.75
1.05
1.25
0.1
3
2
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y 200(l.03)t
y 200(l.03)5
y 200(l.03)1
y 200(l.03)2
y 231.55
y 206
y 212.18
a. Your balance will be 206 after 1 year. b.
Your balance will be 212.18 after 2 years. c.
Your balance will be 231.55 after 5 years.
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2
2.5
3.13
3.91
Practice on your calculator. Your key entry for
the previous problem is this 2(5/4)t Substitut
e 0,1,23 for t
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8-5 Write and Graph Exponential Growth Models
Exponential Function y abx a is not equal
to 0. b gt 0 b is not equal to 1. For Exponential
Growth , b gt 1.
Dont forget the homework form!