MATH 1030-005
Homework #8
Instructions: Answer the following questions on a separate sheet of paper.
1. Suppose that the population of ants in Pollyanna’s ant colony is decreasing at a rate of 3% per
year.
(a) If she has 1500 ants in 2008, how many will there be in 2060?
(b) If she has 1500 ants in 2008, how many were there in 1999?
(c) In what year will the number of ants drop below 1000?
(d) What is the half-life of the population of Pollyanna’s ant colony?
2. Suppose that the population of ants in Felix’s ant colony is increasing at a rate of 6% per day.
(a) If Felix buys 20 ants, how many will he have in 3 weeks?
(b) When will Felix’s ant colony reach a population of 100?
(c) How often does the number of ants double?
3. Suppose that Pollyanna has a viral infection that is being treated by some herbal remedy, and
that the number of viruses is cut in half every 3 days.
(a) What percentage of the original viruses are left after 2 weeks?
(b) After how many days will the number of viruses be at 16% of the original number?
(c) What is the daily decay rate of the viruses? (Hint, use t= 1 day.)
4. Suppose that Felix has a viral infection that just won’t go away no matter what he tries, and
that the number of viruses doubles every 25 weeks.
(a) If Felix’s infection consists of a modest 22 viruses right now, how many viruses will he have in
5 weeks?
(b) If Felix’s infection consists of 22 viruses right now,, how many viruses were infecting him 1
week ago?
(c) How many weeks will pass until the infection reaches 10,000 viruses?
5. Suppose a quantity Q grows exponentially at a rate of 18% per decade. Compute the doubling
time of this growth.
6. Suppose a quantity R decays exponentially at a rate of 44% per month. Compute the half-life
of this decay.
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