1
1. Population Growth. The 2000 census found a U.S. population of about 281 million, with an
estimated growth rate of 0.7% per year. Write an equation for the U.S. population that assumes
exponential growth rate at this rate. Use the equation to predict the U.S. population in 2100.
Q = U.S. population
Q0 = initial value is the 2000 population = 281 million
r = 0.7% per year = 0.007 per year
Q = Q0 x (1 + r)t
= 281 million x (1 + 0.007) t
= 281 million x (1.007) t
Use the equation to predict the U.S. population in 2100:
= 281 million x (1.007) 100 = 564 million
2.
a. Create an exponential function of the form Q = Q0 x (1 + r)t to model the situation described.
Be sure to identify both variables in your function.
b. Create a table showing the values of the quantity Q for the first 10 units of time
c. Make a graph of the exponential function
The population of a town with an initial population of 60,000 grows at a rate of 2.5% per year.
Q = population of _______________________
Q0 = initial value of the population is _____________
r = 2.5% per year = _____________
Q = Q0 x (1 + r)t
Q = 60,000 x (1 +
Year
0
1
2
3
4
5
6
7
8
9
10
)t
Population
Chapter 9C Practice Problems
2
Chapter 9C Practice Problems
3
3. Declining Population. China’s one-child policy was originally implemented with the goal of
reducing China’s population to 700 million by 2050. China’s population was about 1.2 billion.
Suppose China’s population declines at a rate of 0.5% per year. Write an equation for the
exponential decay of the population. Will this rate of decline be sufficient to meet the original
goal?
Q = China’s population
Q0 = initial value of the population is
r = -0.5% per year =
Q = Q0 x (1 + r)t
4.
a. Create an exponential function of the form Q = Q0 x (1 + r)t to model the situation described.
Be sure to identify both variables in your function.
b. Create a table showing the values of the quantity Q for the first 10 units of time
c. Make a graph of the exponential function
A town with a population of 10,000 is losing residents at a rate of 0.3% per month because of a
poor economy.
Q = population of _______________________
Q0 = initial value of the population is _____________
r = _____% per year = _____________
Q = Q0 x (1 + r)t
Q = _______ x (1 +
Month
0
1
2
3
4
5
6
7
8
9
10
)t
Population
Chapter 9C Practice Problems
4
Chapter 9C Practice Problems