First Order 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 \(P(\ln3)?\)