Question

# (a)If the birth rate and death rate of the number of bacteria are proportional to the number of bacteria present, what is the population as a function of time. (b)What is the limiting situation for increasing time? Interpret it.

Solution

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a) Let $k_1$ be the constant of proportionality for the birth rate, $k_2$ the constant of proportionality for the death rate, and $y(t)$ the population at time $t$.

According to the given data, we obtain the ODE

$y' (t)= k_1y(t) - k_2y(t).$

This is the mathematical model of the biological process.

Let's solve the ODE.

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