Can Someone Please Help Me!!
"Suppose the population P(t), measured in millions of people, of a country satisfies the differential equation dP/dt = kP(230-P) with k constant. Its population in 1940 was 135 million and was then growing at the rate of 1 million per year. Predict this country's population for the year 1991.

Question

Can Someone Please Help Me!!
"Suppose the population P(t), measured in millions of people, of a country satisfies the differential equation dP/dt = kP(230-P) with k constant. Its population in 1940 was 135 million and was then growing at the rate of 1 million per year. Predict this country's population for the year 1991.

anonymous · Answer

1=K*135*(230-135)
k=1/12825
dp/dt=(1/12825)*p*(230-p)
 ∫1/p*(230−p)dp=∫1/12825dt
  
∫1/(230∗p)−1/(230∗(230−p))dp=∫1/12825dt

(1/230)∗ln|p|+(1/230)∗ln|230−p|=1/12825∗t+c

(12825/230)*{ln|x|+ln|(230-x)|-ln|135|-ln|(230-135)|}=1991-1940

x is the required answer

anonymous · Answer

Thank you! Also when I solved for  x I got 201.68 which is wrong, can you please tell me what you got and how you did it?

anonymous · Answer

There is a small mistake in above solution.After correcting it last line should be
 (12825/230)*{ln|x|-ln|(230-x)|-ln|135|+ln|(230-135)|}=1991-1940

ln|x|-ln|230-x|=(51*230/12825)+ln|135|-ln|(230-135)|
ln|x|-ln|230-x|=1.266
ln|x/(230-x)|=1.266
x/(230-x)=3.546
x=179.4139

anonymous · Answer

thank you!!! but sadly that isnt the correct the answer!

anonymous · Answer

what is the correct answer ?

anonymous · Answer

It's not given! It's an online hw assignment and it just tells you if youre wrong or right! :/ I'm going to ask my professor and see what went wrong bc i too got 179