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Lynn uses this equation to model the growth of a bacteria culture. She let N represent the number of bacteria present after t hours of growth. N equals 100 e Superscript k t Baseline There were 400 bacteria present after 5 hours of growth.QuestionWhich is equal to the value of k?

Lynn uses this equation to model the growth of a bacteria culture She let N represent the number of bacteria present after t hours of growth N equals 100 e Supe class=

Respuesta :

Given:

There are given the equation:

[tex]N=100e^{kt}[/tex]

Explanation:

From the given exponential function, N represents the number of bacteria and t represents the time.

Then,

According to the question, the value of N is 400 and the value of t is 5.

So,

Put the value of N and t into the above expression to find the value of k.

Then,

[tex]\begin{gathered} N=100e^{kt} \\ 400=100e^{k(5)} \end{gathered}[/tex]

Then,

[tex]\begin{gathered} 400=100e^{k(5)} \\ \frac{400}{100}=\frac{100e^{5k}}{100} \\ 4=e^{5k} \end{gathered}[/tex]

Then,

[tex]\begin{gathered} 4=e^{5k} \\ 5k=ln(4) \\ k=\frac{ln(4)}{5} \end{gathered}[/tex]

So,

The value of k is shown below:

[tex]k=\frac{ln(4)}{5}[/tex]

Final answer:

Hence, the correct option is D.

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