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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Answered 3 months ago
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a) Let k1k_1 be the constant of proportionality for the birth rate, k2k_2 the constant of proportionality for the death rate, and y(t)y(t) the population at time tt.

According to the given data, we obtain the ODE

y(t)=k1y(t)k2y(t).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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