Warm Up

1
Warm Up Simplify each expression. 1. (4
0.05)2 3. 4. The first term of a geometric
sequence is 3 and the common ratio is 2. What
is the 5th term of the sequence? 5. The function
f(x) 2(4)x models an insect population after x
days. What is the population after 3 days?
2. 25(1 0.02)3
16.4025
26.5302
1.0075
48
128 insects
2
Graph y 3x2 6x 1.
Find the axis of symmetry.
The axis of symmetry is x 1.
1
The vertex is (1, 2).
Find the vertex.
y 3(1)2 6(1) 1
3 6 1
2
Find the y-intercept.
(0, 1).
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Objective
Solve problems involving exponential growth and
decay.
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Exponential growth occurs when a quantity
increases by the same rate r in each period t.
When this happens, the value of the quantity at
any given time can be calculated as a function of
the rate and the original amount.
5
The original value of a painting is 9,000 and
the value increases by 7 each year. Write an
exponential growth function to model this
situation. Then find the paintings value in 15
years.
6
A sculpture is increasing in value at a rate of
8 per year, and its value in 2000 was 1200.
Write an exponential growth function to model
this situation. Then find the sculptures value
in 2006.
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A common application of exponential growth is
compound interest. Recall that simple interest is
earned or paid only on the principal. Compound
interest is interest earned or paid on both the
principal and previously earned interest.
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Write a compound interest function to model each
situation. Then find the balance after the given
number of years.
1200 invested at a rate of 2 compounded
quarterly 3 years.
10
Write a compound interest function to model each
situation. Then find the balance after the given
number of years.
15,000 invested at a rate of 4.8 compounded
monthly 2 years.
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Write a compound interest function to model each
situation. Then find the balance after the given
number of years.
1200 invested at a rate of 3.5 compounded
quarterly 4 years
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Write a compound interest function to model each
situation. Then find the balance after the given
number of years.
4000 invested at a rate of 3 compounded
monthly 8 years
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Exponential decay occurs when a quantity
decreases by the same rate r in each time period
t. Just like exponential growth, the value of the
quantity at any given time can be calculated by
using the rate and the original amount.
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Notice an important difference between
exponential growth functions and exponential
decay functions. For exponential growth, the
value inside the parentheses will be greater than
1 because r is added to 1. For exponential decay,
the value inside the parentheses will be less
than 1 because r is subtracted from 1.
15
The population of a town is decreasing at a rate
of 3 per year. In 2000 there were 1700 people.
Write an exponential decay function to model this
situation. Then find the population in 2012.
16
The fish population in a local stream is
decreasing at a rate of 3 per year. The original
population was 48,000. Write an exponential decay
function to model this situation. Then find the
population after 7 years.
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A common application of exponential decay is
half-life of a substance is the time it takes for
one-half of the substance to decay into another
substance.
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Astatine-218 has a half-life of 2 seconds.
Find the amount left from a 500 gram sample of
astatine-218 after 10 seconds.
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Bismuth-210 has a half-life of 5 days.
Find the amount of bismuth-210 left from a
100-gram sample after 5 weeks. (Hint Change 5
weeks to days.)
HW pp. 785-788/10-20,23-33 Odd,35-48,50,52,54,55-6
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