Question

A population of bacteria is growing according to the equation P (t)=1100e^0.04t. Estimate when the population will exceed 1455.

Answer 1

`p(t)=1100e^(0.04t)`

We want to estimate the population when the population exceed 1455

Set p(t) = 1455 and solve for t

`\begin{gathered} 1100e^(0.04t)=1455 \\ Divide\text{ both sides by 1100} \\ (1100e^(0.04t))/(1100)=(1455)/(1100) \\ \\ e^(0.04t)=1.322727 \\ lne^(0.04t)=ln1.322727 \\ 0.04t=0.27763 \\ t=(0.27763)/(0.04) \\ t=6.99 \end{gathered}`

Thus, the population will exceed 14551 after 6.99 years