Sections 6.7 and 6.8
Name____________________________________
1) A new water treatment plant reduces pollutants in the water by 1/50 each day. How
long until only 1/100 of the original pollutants remain?
2) A certain species of bird is in danger of extinction. It is estimated that only 900 of the
birds are alive today. Five years ago there were 1200. Experts believe that if the
population drops below 200, extinction is assured. How many years from now is this
expected to happen?
3) Carbon 14 has a half life of 5750 years. Suppose there are 200 grams of Carbon 14 in
an organism that dies today. In how many years will only 75 grams of the Carbon 14
remain?
4) If inflation persists at 4% compounded continuously, how much will an item that costs
$10.00 today cost in 5 years?
5) How much money must be placed in an account that earns 4.5% compounded
continuously in order that $1000 may be withdrawn at the end of the year each year
forever?
6) There were 3000 freshmen at UNM in thefall of 2006. In the fall of 2005 there were
2950 freshman. Assuming that the growth of the freshman class obeys uninhibited
exponential growth, how many freshmen will there be in 2020?
7) The local bank has three options for your investments. The first is a bond which pays
triple your investment once at the end of 20 years. The second is an account which pays
5.4% compounded continuously. The third is an account which pays 5.5% compounded
monthly. Which one will be the best value for you? (hint: Assume that you invest $1.00
in each case. Compare amounts at the end.)
8) If the average yearly sales for a retail mall increases according to the formula
A  A0 e .0324t (where t is measured in years.)
How long until the sales are 125% of this year’s?