# 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?

##### 1 Answer

a)

#### Explanation:

a) The initial population of the town is simply

The initial population is

b) The amount of people in the town after

There are

c) The rate of change of people after

To differentiate, let's rewrite a little, recalling that

Differentiate, using the Chain Rule:

Recalling that

The rate of change after a week is