Calculus

First Order Differential Equations

Logistic Differential Equations

         

Given the logistic differential equation dPdt=3P(1P600), \frac{dP}{dt} = 3 P \left( 1 - \frac{P}{600}\right), and P(0)=P0=17,P(0)=P_{0} = 17, what time tt satisfies P(t)=100?P(t)=100?

Let P0P_0 denote the initial value P(0)P(0) of the function P(t).P(t). Which of the following functions satisfy dPdt=5P(1P8)? \frac{dP}{dt} = 5 P \left( 1 - \frac{P}{8}\right)?

Consider the logistic differential equation dPdt=ln2×P(1P5). \frac{dP}{dt} = -\ln 2 \times P \left( 1 - \frac{P}{5}\right). If P(4)=28,P(4) = 28, what is the value of P(0)P(0)?

Given the logistic differential equation dPdt=ln2×P(1P18), \frac{dP}{dt} = -\ln 2 \times P \left( 1 - \frac{P}{18}\right), if P(0)=P0=14,P(0)=P_{0} = 14, what is the value of P(4)?P(4)?

Given the logistic differential equation dPdt=2P(1P21),\displaystyle{ \frac{dP}{dt} = -2 P \left( 1 - \frac{P}{21}\right)}, if P(0)=P0=18,P(0)=P_{0} = 18, what is the value of P(ln3)?P(\ln3)?

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