Question

A population of bacteria is growing according to the equation P(t) = 1850e ^ (0.09t). Estimate when the population will exceed 2402t=Give your answer accurate to one decimal place.

Answer 1

We will have the following;

`\begin{gathered} 2402=1850e^(0.09t)\Rightarrow(2402)/(1850)=e^(0.09t)\Rightarrow(1201)/(925)=e^(0.09t) \\ \\ \Rightarrow ln((1201)/(925))=0.09t\Rightarrow t=(ln(1201/925))/(0.09) \\ \\ \Rightarrow t=2.901289829...\Rightarrow t\approx2.9 \end{gathered}`

So, the population will exceed 2402 bacteria after 2.9 units of time.