EXPONENTIAL DECAY

Be sure you have reviewed the meanings of factor and percentage change.

Recall the two equations for exponential growth and decay:

Suppose some environmental stress reduced a population of 1000 wee beasties to 800 in two days. How many will there be 7 days after the intial count of 1000 wee beasties?

This problem must be done in two steps. First, we use the information about the first 2 days to find the decay constant, 'k'. Second, we use 'k' and the time t = 7 days, and the intial population to find the final population.

For the first step, the logarithmic form of the equation is most useful. We know '' (the initial population was 1000), 'N' (the final population was 800), 't' (the time period was 2 days). Substituting into the second equation, we get

So our decay constant is k = -0.112 day.

Now we can do the second step. This time, the first equation (the exponential form of the equation) will be easier. Substituting k = -0.112 day, t = 7 day, and  = 1000, we get

You should be able to get N = 457 wee beasties after 7 days.

Exponential Growth