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

Answer:

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

Step-by-step 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:

$\frac{dP}{dt} = kP$

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 $P(0) = 1000$