Andy C. answered 11/01/17
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p(t) = 20(4t+3)/(2t+5)
Examining the long term behavior, divides each term by t:
20 ( 4 + 3/t)/ (2 + 5/t)
As t grows infinitely large, the long term behavior is 20*4/2 = 40 which shows the population increases...
20(4t +3)/(2t +5 ) = 50
20(4t + 3) = 50(2t+5)
80t + 60 = 100t + 250
0 = 100t + 250 - 80t - 60
0 = 20t + 190
-190 = 20t
t = -190/20 = -19/2
No, i cannot reach 50 as the result is negative time.
The long term behavior shows that for infinitely large time t,
the function limit is 40.