# Growth/Decay Problems for Precalculus Students

### Professor Rothchild, MAT172, Lehman College, CUNY

1.There are 100 bacteria in a culture, and the number of bacteria triples every 5 hours.
a) How many will there be in 30 hours?
b) Write a function, N, that gives the number of bacteria t hours from now.
c) In how many hours will there be 1800 bacteria?
2. The population of West Oblivion was 600 in 1850 and is known to double every 25 years.
a) What was the population in 2000?
b) Write a function, P, that gives the population y years after 1850.
c) In what year did the population first exceed 4000?
3.A bank account receives 3% annual interest compounded quarterly.
a) If \$1000 is deposited into the account initially and no other deposits are made, write a formula for A, the amount of money in the account after t years.
b) How many years will it take for the amount of money in the account to double?
4. A population increases by 2.5% per year. In how many years will the population double?

5. An investment involvinga single deposit pays 6% per year, compounded annually. What deposit is needed to have\$100,000 after 18 years?

6.Five hours after the start of an experiment, there were 600 bacteria, and 5 hours after that there were 720 bacteria. Write a formula for N, the number of bacteria t hours after the start of the experiment,

a) assuming that N is a linear function of it.
b) assuming that N is an exponential function t.
c) In each of the above cases, how many bacteria were there at the start?
7. The half-life of joannium is 3 days. A sample consists of 60 grams.
a) How much remains after 12 days? After t days?
b) In how many days will 50 grams have decayed?
8. 90% of a sample of a radioactive element remains after 7 days. Find the half-life of the element.

9. The half-life of carbon-14 is about 5730 years. How long would it take for a sample to decay to 10% of the original amount?

10. Suppose the value of the dollar decreases at the rate of 3% per year. In how many years will todays dollar lose half its value?