Using Logistic Differential Equation
In Exercises 13-16, the logistic differential equation models the growth rate of population. Use the equation to (a) find the value of k, (b) find the carrying capacity; (c) use a computer algebra system to graph a slope field, and (d) determine the value of P at which the population growth rate is the greatest:
13. dP/dt = 3P - 0.1SP
14. dP/dt = 100P(1 - P/250)
15. dP/dt = 0.1P - 0.0004P^2
16. dP/dt = 0.4P - 0.0025P^2