Question

Question 3<>600e0.06. Estimate when the.A population of bacteria is growing according to the equation P(t)population will exceed 745.t =Give your answer accurate to at least one decimal place.Question Help: Video Message instructorSubmit Question

Answer 1

Given:

`P(t)=600e^(0.06t)`

To get the time when the population will exceed 745:

`\begin{gathered} when\text{ }P(t)=745, \\ 745=600e^(0.06t) \\ Divide\text{ both sides by 600;} \\ (745)/(600)=e^(0.06t) \\ 1.2417=e^(0.06t) \\ Take\text{ the natural logarithm of both sides;} \\ \ln1.2417=0.06t \\ Divide\text{ both sides by 0.06;} \\ (\ln1.2417)/(0.06)=t \\ t=3.608 \\ \\ To\text{ one decimal place;} \\ t\approx3.6 \end{gathered}`

Therefore, the time it will take for the population to exceed 745 is 3.6