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 Return to: Exponential Growth and Decay Menu Exit to: Physics Tutorial Menu