## Growth/Decay Problems for Precalculus Students

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

- There are 100 bacteria in a culture, and the number of bacteria triples every 5 hours.
- How many will there be in 30 hours?
- Write a function, N, that gives the number of bacteria t hours from now.
- In how many hours will there be 1800 bacteria?

- The population of West Oblivion was 600 in 1850 and is known to double every 25 years.
- What was the population in 2000?

- Write a function, P, that gives the population y years after 1850.

- In what year did the population first exceed 4000?

- What was the population in 2000?
- A bank account receives 3% annual interest compounded quarterly.
- 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.

- How many years will it take for the amount of money in the account to double?

- 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.
- A population increases by 2.5% per year. In how many years will the population double?
- An investment involvinga single deposit pays 6% per year, compounded annually. What deposit is needed to have$100,000 after 18 years?
- 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,
- assuming that N is a linear function of it.

- assuming that N is an exponential function t.

- In each of the above cases, how many bacteria were there at the start?

- assuming that N is a linear function of it.
- The half-life of joannium is 3 days. A sample consists of 60 grams.
- How much remains after 12 days? After t days?

- In how many days will 50 grams have decayed?

- How much remains after 12 days? After t days?
- 90% of a sample of a radioactive element remains after 7 days. Find the half-life of the element.
- 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?
- 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?

Last modified: Oct 13, 2011