Question

the population of a town increases at a rate proportional to its population with an initial population of 1000. The corect initial value problem for the population p(t) as a function of time is

Answer 1

This means that the correct initial value problem for the population p(t) as a function of time is is
`P(0) = 1000`

Explanation:

The population of a town increases at a rate proportional to its population:

This means that this situation is modeled by the following differential equation:

`(dP)/(dt) = kP`

In which k is the growth rate.

By separation of variables, the solution is given by:

`P(t) = P(0)e^(kt)`

In which P(0) is the initial population.

Initial population of 1000.

This means that the correct initial value problem for the population p(t) as a function of time is is
`P(0) = 1000`