1­13­16 P.7 Alg M3L6 and L7 Exponential Growth and Decay word problems.notebook
January 13, 2016
Exercises
1. Identify the initial value in each formula below,
and state whether the formula models exponential growth
or exponential decay. Justify your responses.
a)
b)
c)
d)
Date:
Student Outcomes
-
Students compare linear and exponential models of population growth.
Student Outcomes
-Students describe and analyze exponential decay models; they recognize that
in a formula that models exponential decay, the growth factor b is less than 1;
or, equivalently, when b is greater than 1, exponential formulas with
negative exponents could also be used to model decay.
Remember...
The value of the base of the exponential function
determines how fast the increase or growth occurs.
However, when the base was a fraction 0 < base < 1,
the function became decreasing or decaying.
y = ax
y = ax
e)
Again...
Since the base of an exponential function determines
whether the function is a growth or decay model...
AND
we know the formula for exponential growth is:
F(t) = PV(1 + r)t
or
F(t) = a(b)t
What would you expect to be different in the exponential
decay formula?
F(t) = PV(1 - r)t
where a > 1
where 0 < a < 1
1­13­16 P.7 Alg M3L6 and L7 Exponential Growth and Decay word problems.notebook
January 13, 2016
Example 1. POPULATION Example 2. DEPRECIATION The population of Bulgaria has been decreasing at an annual rate of 1.3%. If the population of Bulgaria was about 7,797,000 in the year 2000, predict its population in the year 2010. Source: U. S. Census Bureau
Carl Gossell is a machinist. He bought some new machinery for about $125,000. He wants to calculate the value of the machinery over the next 10 years for tax purposes. If the machinery depreciates at the rate of 15% per year, what is the value of the machinery (to the nearest $100) at the end of 10 years?
Homework:
1. A construction company purchased some equipment costing
$300,000. The value of the equipment depreciates
(decreases) at a rate of 14% per year.
Example 3 POPULATION For Exercises 1 and 2, use the following information.
The population of New York City increased from 7,322,564 in 1990 to 8,008,278 in 2000. The annual rate of population increase for the period was about 0.9%. Source: www.nyc.gov
a. Write a formula that models the value of the equipment
each year.
1. Write an equation for the population t years after 1990.
2. Use the equation to predict the population of New York City in 2010.
b. What is the value of the equipment after 9 years?
c. Estimate when the equipment will have a value of $50,000.
1­13­16 P.7 Alg M3L6 and L7 Exponential Growth and Decay word problems.notebook
January 13, 2016
2. The number of newly reported cases of HIV (in
thousands) in the United States from 2000 to 2010 can be
modeled by the following formula:
where t is the number of years after 2000.
a.
WEIGHT TRAINING For Questions 3 and 4 use the
following information.
In 2007, there were 43.2 million people who used free weights.
3) Assuming the use of free weights increases 6%
annually, write an equation for the number of people using
free weights t years from 2007.
Identify the growth factor.
b. Calculate the estimated number of new HIV
cases reported in 2004.
5) Determine the amount of an investment if $250 is
invested at an interest rate of 10.3% compounded annually for
40 years.
4)
Predict the number of people using free weights in 2017.