Problema Solution
The population of wolves in a state park after t years is modeled by he function p(t)=400/ 1+99e^-.03t. When will the number of wiles be 100?
Answer provided by our tutors
P(t) = 400 / [ 1 + 99 e^( - 0.3 t ) ]
In this case P ( t ) = 100
=> 400 / [ 1 + 99 e^(-0.3t ) ] = 100
=> 1 + 99 e^( - 0.3 t ) = 4
=> 99 e^( - 0.3 t ) = 3
=> e^( - 0.3 t ) = 3/99 = 1/33
=> e^ ( 33 t ) = 33
Taking log(n) -----
=> ln ( 33 ) = 33 t
=> t = ln ( 33 ) divided by 33
=> t = 3.4965 / 33 = 0.1059 years . answer