Exponential Models of
Population Growth/Decay
Homework Assignment
Directions: Recall that an exponential model is one of the form y = a(b)x where a is
the starting value or population and b is the rate at which it’s increasing or decreasing.
You will now explore other types of population growth and decay.
1. a. In the equation y = 12(1.8)x what is the beginning population?
_________________
b.In the equation above, is the population increasing or decreasing? How can you
tell?
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c. In the equation above what is the rate?
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d. Make up a situation in which this equation could model a population.
2. A herd of buffalo began with a population of 100,000. The average birth rate has been
25% per year, but the death rate has been 48% per year.
a. What is the difference between the birth rate and death rate?
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b. Is the population increasing or decreasing? How do you know?
_________________________________________________________________
c. Write an exponential equation that models this situation, letting y represent the
population and x represent the time in years.
__________________
d. Assuming that these rates stay the same and there are no other factors, how
long will it take the population to fall below 5000? (Round the answer to the nearest
year.)
___________________
e. Sketch a graph of the exponential equation that models this situation.
3. As a scientist, you have been observing a monkey population in the jungle. When you
began, there were 1250 monkeys. Over time, you’ve observed that the birth rate seems to
be about 45% per year and the death rate seems to be about 28% per year.
a. What is the difference between the birth rate and death rate?
___________________
b. Is the population increasing or decreasing? How do you know?
________________________________________________________________
c. Write an exponential equation that models this situation, letting y represent the
population and x represent the time in years.
__________________
d. Assuming that these rates stay the same and there are no other factors, how
long will it take the population to reach 5000? (Round the answer to the nearest year.)
___________________
e. Sketch a graph of the exponential equation that models this situation.
4. Given the following data from a large mouth bass population in a local pond below,
find the exponential equation that models this situation. Let 0 represent the year 1970.
YEAR
POPULATION
1970
200
1975
322
1980
519
1985
836
1990
1346
1995
2167
2000
3490
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Exponential Models of
Population Growth/Decay
Homework Key
1.
a. 12
b. Increasing. The growth rate or base of the exponential is greater than 1.
c. 1.8 or the student might say growing at a rate of 80%.
d. Any kind of situation that involves a population growing at a rate of 80%.
2. a. 23%
b. Decreasing. The death rate is higher than the birth rate.
c. Y = 100,000(.77)x
d. 12 years
e. Any sketch that’s close would be acceptable.
3.
a. 17%
b. Increasing. The birth rate is higher than the death rate.
c. Y = 1250(1.17)x
d. 9 years
e. Any sketch that’s close would be acceptable.
4. Y = 200(1.10)x