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1 Nov 2021

Given information

Given that the protozoa population grows with a steady relative growth rate of  per member each day. 

Also, given that on day zero population of protozoa  

Step-by-step explanation

Step 1.

Observe that the population of protozoa on day zero was .

Given the steady relative growth rate of  per member each day, then 

Do differential equation by the given information

Let be the population size and   be the time in hours.

   

 

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\[\begin{array}{l}
\;\;\int {\frac{{dP}}{P} = \int {0.7944dt} } \\
\ln \left| P \right| = 0.7944t + C\\
{\rm{integrate both sides}}\\
\left| P \right| = {e^{0.7944t + C}}\\
\left| P \right| = {e^C} \times {e^{0.7944t}}\\
P = C{e^{0.7944t}}{\rm{         }}\left( {{\rm{raise to the }}{e^x}{\rm{ power}}} \right)\\
2 = C{e^{0.7944 \times 0}}\\
2 = C \times 1\\
2 = C\\
P = 2 \times {e^{0.7944 \times 6}}\\
P = 234.991\;\;\;
\end{array}\]

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