homework help?

Question

DDT is an insecticide that has been used by farmers. It decays slowly and is sometimes absorbed by plants that animals and humans eat. experimental data shows that 10% of the initial amount is eliminated in 5 years. using this information answer the following questions.
A. What is the rate of decay?
B. What percent of the original amount of DDT is left after 10 years?
C. The U.S. environmental protection agency banned almost all use of DDT in the U.S. in 1972. If a lake was polluted with DDT and none has been used near the lake since it was banned, in what year will the concentration of DDT fall below 25%?





does anyone have any idea how to do this??? please try and show work if you can.

Answer 1

a.) Start with what we know: at 5 years, there is 90% left.
Let's define the rate of decay as x%/year, and use t for time (in years). We can then set up a formula:
amount left = (1 - x)^t
Given what we know:
90% = (1 - x)^5
.9 ^1/5 = 1-x = 0.979148...
x = 1 - 0.979148... = 0.020852 = 2.0852%.

b.) To solve this, plug the rate of decay back into the formula we set up, and set t = 10.

c.) To solve this, plug the rate of decay back into the formula, set the amount left to .25:
.25 = 0.979148^t

Then, take the log of both sides. This will give you a logarithm on both sides - on the left, you have a logarithm where t is in the exponent. This lets you distribute t out of the log (because log a^b = b log a), and you can set t equal to the log of .25 and the log of 1-x.