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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §6.5 Separable Equations Including the Logistic Equation, #19 · Differential Equations · First-order

Suppose Pittsburgh grows from … million people in 1900 to … million…

Suppose Pittsburgh grows from $y_{0} = 1$ million people in 1900 to $y = 3$ million in the year 2000. If the growth rate is $y^{'} = 12, 000$ /year in 1900 and $y^{'} = 30, 000$ /year in 2000, substitute in the logistic equation to find $c$ and $b$ . What is the steady state? Extra credit: When does $y = y_{\infty} /2 = c /2 b$ ?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §6.5 Separable Equations Including the Logistic Equation, #19

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