Answer
t = ln (2.3) / 2
Explanation:
y(t) = 40 e^2t + 8
Let y(t) = total population within a time frame
According to the question, y(t) = 100
100 = 40 e^2t + 8
Collect the like terms
100 - 8 = 40 e^2t
92 = 40 e^2t
Divide both sides by 40
92/40 = 40 e^2t / 40
2.3 = e^2t
Take the natural logarithms of both sides
ln (2.3) = ln (e^2t)
ln (2.3) = 2t
Divide both sides by 2
ln (2.3) / 2 = 2t / 2
t = In (2.3) / 2 in terms of the natural logarithms
t = 0.8329 / 2
t = 0.4 mins
