Question

A population of bacteria is growing according to the equation P(t)=600e0.03t . In how many years will the population will exceed 708? Round your answer to one decimal place.t =

Answer 1

Given

`P=600e^(0.03t)`

Find

time,t

Explaination

`\begin{gathered} P=600e^(0.03t) \\ 708=600e^(0.03t) \\ 1.18=e^(0.03t) \end{gathered}`

Taking log on both sides

`\begin{gathered} ln(1.18)=0.03t \\ 0.165514438=0.03t \\ t=5.5\text{ sec} \end{gathered}`

Final Answer

t = 5.5 sec