The population of a town a town after t weeks is given by p(t)=1200(2^-t). a) what is the initial population of the town? b) how many people are there after 1 week? c) what is the rate of change of people after 1 week?
a) The initial population of the town is simply
The initial population is
b) The amount of people in the town after
c) The rate of change of people after
To differentiate, let's rewrite a little, recalling that
Differentiate, using the Chain Rule:
The rate of change after a week is