The rate of growth of a particular population is given by dP/dt = 50t^2 - 100t^(3/2) , where P is population size and t is the time in years. Assume the initial population is 25,000. Determine the population function, P(t).

Question

The rate of growth of a particular population is given by dP/dt = 50t^2 - 100t^(3/2) , where P is population size and t is the time in years.  Assume the initial population is 25,000.  Determine the population function, P(t).

kagıtucak · Answer

I cannot see the equation after the phrase "given by"

anonymous · Answer

sorry about that!

kagıtucak · Answer

You can take the integral of dP/dt to get the function P(t). Lets do it:
P(t)=(50/3)*(t^3/3)-(100*2/5)*(t^(5/2))+c
P(t)=(50/3)*(t^3/3)-(40)*(t^(5/2))+c
We are given that initial population is 25000. Lets put it in t=0:
25000=0-0+c
c=25000
Hence,
P(t)=(50/3)*(t^3/3)-(40)*(t^(5/2))+25000
Hope I didnt make a mistake:)