Question 1163015: The population P of a certain small-town t years from now is predicted to be p(t)=35000 + 10000/(t+2)^3 . In your own method estimate the population of the town in the long run.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the equation is p(t) = 35000 + 10000 / (t+2)^3
as t becomes progressively larger, the expression 10000 / (t + 2) ^ 3 becomes progressively smaller until it approaches 0.
this means the population will approach 35,000 in the long run.
for example:
when t = 0, the formula becomes p(t) = 35000 + 10000 / 2^3 = 36250
when t = 100, the formula becomes p(t) = 35000 + 10000 / 102^3 = 35000.99842,
the larger t gets, the close to 35000 p(t) gets.
|
|
|
