Lesson
Applications (2)
Solve the problem.
1) The population of a particular country was 25 million in 1981; in 1996, it was 31 million. The
exponential growth function A = 25ekt describes the population of this country t years after 1981.
Use the fact that 15 years after 1981 the population increased by 6 million to find k to three decimal
places.
2) How long will it take for the population of a certain country to double if its annual growth rate is
3.5%? Round to the nearest year.
3) The number of books in a small library increases according to the function B = 6700e0.04t, where t
is measured in years. How many books will the library have after 5 year(s)?
4) How long will it take for prices in the economy to double at a 7% annual inflation rate? (Round to
the nearest year.)
5) The population of a particular city is increasing at a rate proportional to its size. It follows the
function P(t) = 1 + ke0.06t where k is a constant and t is the time in years. If the current population
is 14,000, in how many years is the population expected to be 35,000? (Round to the nearest year.)
6) The half-life of plutonium-234 is 9 hours. If 40 milligrams is present now, how much will be
present in 5 days? (Round your answer to three decimal places.)
7) The function A = A0e-0.01155x models the amount in pounds of a particular radioactive material
stored in a concrete vault, where x is the number of years since the material was put into the vault.
If 800 pounds of the material are initially put into the vault, how many pounds will be left after 180
years?
8) How long will it take a sample of radioactive substance to decay to half of its original amount, if it
decays according to the function A(t) = 450e-0.157t, where t is the time in years? Round to the
nearest hundredth year.
9) A certain radioactive isotope has a half-life of approximately 1800 years. How many years would
be required for a given amount of this isotope to decay to 55% of that amount?
10) A certain radioactive isotope decays at a rate of 0.175% annually. Determine the half-life of this
isotope, to the nearest year.
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