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Exponential Growth and Decay- HW Problems
1. A population of a town today is 100,000. The town’s population
three years from now is expected to be approximately 135,000.
Assuming that the population growth is exponential:
a. find the annual relative growth rate.
b. At this growth rate how long does it take the town’s population to
double?
c. Find the absolute growth rate (i.e., 𝑃′(𝑡)) of the population when it
has doubled.
2. A certain bacteria culture grows at a rate proportional to its size.
After 2 hours the number of bacteria was 600 and after 6 hours it was
38,400.
a. Find the relative growth rate.
b. what was the size of the population at 𝑡 = 0?
c. Find a formula for the size of the population at time 𝑡.
d. Find the number of bacteria after 4 hours.
e. What is the absolute rate of growth of the population at
𝑡 = 4 hours.
f. When will the population reach 75,000?
Exponential Growth and Decay- HW Problems
1. A population of a town today is 100,000. The town’s population
three years from now is expected to be approximately 135,000.
Assuming that the population growth is exponential:
a. find the annual relative growth rate.
b. At this growth rate how long does it take the town’s population to
double?
c. Find the absolute growth rate (i.e., 𝑃′(𝑡)) of the population when it
has doubled.
2. A certain bacteria culture grows at a rate proportional to its size.
After 2 hours the number of bacteria was 600 and after 6 hours it was
38,400.
a. Find the relative growth rate.
b. what was the size of the population at 𝑡 = 0?
c. Find a formula for the size of the population at time 𝑡.
d. Find the number of bacteria after 4 hours.
e. What is the absolute rate of growth of the population at
𝑡 = 4 hours.
f. When will the population reach 75,000?
