Question

a population of bacteria is growing according to the equation P(t)=1500e^0.06t in how many years will the population exceed 1965? Round your answer to one decimal placet=

Answer 1

Given

The equation is given as

`P(t)=1500e^(0.06t)`

Explanation

To find the years required to exceed the population 1965.

`\begin{gathered} 1965=1500e^(0.06t) \\ (1965)/(1500)=e^(0.06t) \\ 1.31=e^(0.06t) \end{gathered}`

Take ln both sides.

`\begin{gathered} ln1.31=0.06tlne \\ 0.27002=0.06t \\ t=(0.27002)/(0.06) \\ t=4.5 \end{gathered}`

Answer

Hence the time required in years to exceed the population 1965 is

4.5 years.