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First Order Differential Equations

These are equations, Calculus-style. From modeling real-world phenomenon, from the path of a rocket to the cooling of a physical object, Differential Equations are all around us.

Logistic Differential Equations

Given the logistic differential equation \[ \frac{dP}{dt} = 3 P \left( 1 - \frac{P}{600}\right), \] and \(P(0)=P_{0} = 17,\) what time \(t\) satisfies \(P(t)=100?\)

Let \(P_0\) denote the initial value \(P(0)\) of the function \(P(t).\) Which of the following functions satisfy \[ \frac{dP}{dt} = 5 P \left( 1 - \frac{P}{8}\right)? \]

Consider the logistic differential equation \[ \frac{dP}{dt} = -\ln 2 \times P \left( 1 - \frac{P}{5}\right). \] If \(P(4) = 28,\) what is the value of \(P(0)\)?

Given the logistic differential equation \[ \frac{dP}{dt} = -\ln 2 \times P \left( 1 - \frac{P}{18}\right), \] if \(P(0)=P_{0} = 14,\) what is the value of \(P(4)?\)

Given the logistic differential equation \(\displaystyle{ \frac{dP}{dt} = -2 P \left( 1 - \frac{P}{21}\right)}, \) if \(P(0)=P_{0} = 18,\) what is the value of \(P(\ln3)?\)

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