Question

The population P of a certain small-town t years from now is predicted
to be
3
( 2)
10000 ( ) 35000

 
t
p t . In your own method estimate the
population of the town in the long run.

Answer 1

Answer:

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 3500