Answer:
Step-by-step explanation:
The growth of the population can be modeled by the following differential equation:
Where r is the growth rate, P is the population, and t is the time measures in months.
I am going to solve the above differential equation with the separation of variables method.
Integrating both sides:
Where P(0) is the initial condition
We need to isolate P in this equation, so we do this
So
The problem states that P(0)=3000, so:
The problem wants us to find the value of r:
It states that the population doubles in size from 3000 to 6000 in a 6- month period, meaning that P(6) = 6000. So
To isolate 6r, we apply ln to both sides.
r = 0.1155
The particular solution to the differential equation with the initial condition P(0)=3000 is:
