infinityAnswer:
p(0) = 20
p(5) = 59
Horizontal Asymptote: y = 2400 as t approaches infinity
Explanation:
part C.
To find the horizontal asymptote, we investigate the behaviour of the function p(t) as t approaches infinity.
Now as t approaches inifinty
[tex]P(t)=\frac{60(1+0.4t)}{0.01t+3}[/tex]
the terms 0.04 t and 0.01t become extremely large; so large in fact that we can ignore constant 3 and 1 to get
[tex]P(t)\approx\frac{60\cdot0.4t}{0.01t}[/tex][tex]P(t)\approx2400[/tex]
which means at t -> ∞, p(t) = 2400. In the context of insect population this means that if we wait a long enough time, eventually the insect population will stop decreasing and approach 2400. In other words, the population limit is 2400 insects
