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.

$\begin{gathered} 1965=1500e^{0.06t} \\ \frac{1965}{1500}=e^{0.06t} \\ 1.31=e^{0.06t} \end{gathered}$

Take ln both sides.

$\begin{gathered} ln1.31=0.06tlne \\ 0.27002=0.06t \\ t=\frac{0.27002}{0.06} \\ t=4.5 \end{gathered}$

Answer

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

4.5 years.