Question

A population of bacteria is growing according to the equation P(t)=1600e ^.05t. Estimate when the population will exceed 2282.

Answer 1

To solve the problem we need to use the next given equation:

`P\left(t\right)=1600e^(0.05t)`

If the population will exceed 2282. Then p(x)= 2282.

`2282=1,600e^(0.05t)`

Solve for t:

`(2282)/(1600)=e^(0.05t)`

Now, we need to take logarithms:

`\begin{gathered} \ln((2282)/(1600))=\ln e^(0.05t) \\ \ln((2282)/(1600))=0.05t\ast\ln e \end{gathered}`

Where ln*e = 1.Then:

`\begin{gathered} \ln((2282)/(1600))=0.05t \\ Where \\ t=(\ln((2282)/(1600)))/(0.05) \\ t=7.100 \end{gathered}`

Hence, the population will exceed 2282 when t=7.100