Question

The logistic growth model P(1) -1550represents the population of a bacterium in a culture tube1 + 43.29e-0.334after t hours. What was the initial amount of bacteria in the population?A) 36B) 40C) 34D) 35

Answer 1

Given the logistic growth model

$P(t)=\frac{1550}{1+43.29e^{-0.334t}}$

we want to find the initial amount of bacteria in this problem. If we are talking about the initial amount, we have t = 0 since time doesn't lapse yet for the growth of the bacteria. Hence, for t = 0, the amount of bacteria will be

$\begin{gathered} P(0)=\frac{1550}{1+43.29e^{-0.334(0)}} \\ P(0)=\frac{1550}{1+43.29(1)}=34.9966\approx35 \end{gathered}$