Modeling Town Population Growth Using Separable Differential Equations
A town’s population grows at a rate proportional to its current size. At time \(t=0\), the population is 5000. It is observed that when the population is 5000, it is increasing at a rate of 150 people per year. Set up a separable differential equation to model this situation and solve it by separating variables. […]
Part a
Determine the general antiderivative \(f(t)\) of the rate function \(f'(t) = 2.5t – 1.0\). Use the initial condition \(f(0) = 10\) to find the particular solution for \(f(t)\).