Answer:
P (10) = 65,000
Step-by-step explanation:
Change in population from t=3 to t =5 = 40,000-30,000 = 10,000
The rate of change of the population is given by:
[tex]\frac{dP}{dt} =kP[/tex]
Integrating the above function in the interval t =3 to t =5 gives us the change in population in the period.
[tex]\int\limits^5_3 {\frac{dP}{dt} } \, dt =\int\limits^5_3 {kP} \, dt\\10,000 = (kP*5) - (kP*3)\\kP= 5,000[/tex]
This means that the population increases steadily by 5,000 people each year.
The population for t=10 is:
[tex]P(10) = P(5) +(10-5) kP\\P(10) = 40,000 +(5*5,000)\\P(10) = 65,000[/tex]
