Sometimes insects native to other countries are introduced into the United States by ships carrying imports. This
can be problematic because there are no natural predators to combat the growth of these pests. Scientists use a
model for continuous population growth to project the monthly increase in the number of insects.
Suppose a particular insect came into the United States and, by the time it was discovered at the end of 2016, its
population was estimated to be 2,000. Scientists note that the number of insects continually increases by 15% each
month.
Given the following formula to represent the situation, answer the following questions:
N(t) the number of insects after t months
N(t) = Nert N, the initial number of insects
re rate of growth
te time in months
1) Use the information above to write a function to represent the number of insects present after t
months.
2) Assuming the growth remains continuous, how many insects will there be at the end of 2018? Show your work!
(Hint: Let t= # of months from 2016-2018)
Calculations:
Answer the question in a complete sentence:
3) Assuming the growth remains continuous, when will the number of insects reach one million? Show your
calculations or graphs, including your calculations for the month and year, and then state your answer in a
complete sentence. (Hint: Use the formula given to plug in your values then solve for t using logs.)
Calculations:
Answer the question in a complete sentence: (State your solution for t then figure out the month and year
post the end of 2016)
