Page 177 - How To Solve Word Problems In Calculus

(a) How many bacteria will there be after 3 hours?
(b) How long will it take for the culture to grow to a size of 5000
bacteria?
2. One hour after a bacteria colony starts growing, a scientist
determines that there are 9000 bacteria present. After another
hour, there are 12,000 bacteria. How many bacteria were present
initially?
3. A radioactive substance whose mass is 200 mg will decay to 180 mg
after 12 years. Determine the half-life of this substance.
4. 10 mg of a radioactive substance with a half-life of 20 hours is
injected into a patient’s bloodstream. The patient returns to the
medical facility after 24 hours and a technician determines that
there are 2 mg of the substance in the patient’s pancreas. How
much of the substance is in the remainder of the patient’s
body?
5. An Egyptian papyrus is discovered and it is found that the ratio of
14 12 14 12
Cto C is 65 percent of the known ratio of Cto C in the air
14
today. The half-life of C is 5730 years. How old is the papyrus?
6. How much money will Alexis have in the bank after 3 years if she
invests $700 at 8 percent compounded continuously?
7. How long will it take money to triple if it is compounded
continuously at a rate of 10 percent ?
8. Trevor would like to purchase an engagement ring that sells for
$8000. How much should he put into a savings account today that
pays 5 percent compounded continuously to have enough money to
purchase the ring in 6 months?
9. An ecological study shows that a lake can support a maximum
population of 5000 fish. The logistic function that governs the fish
5000
population is P (t) = where t is measured in months.
1 + 4e −0.4t
(a) How many fish were initially placed into the lake?
(b) How many fish are in the lake after 5 months?
(c) What is the population growth rate after 5 months?
(d) When does the population growth rate of the fish in the pond
begin to decline?
(e) When will the number of fish in the pond be 70 percent of the
pond’s capacity?
10. A public health report states that t weeks after the outbreak of a
new strain of flu, the number of people, in thousands, who will
10
contract the disease is Q(t) = .
1 + 100e −1.5t

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