differential equation
Posted: Thu May 12, 2022 9:02 am
differential equation
Suppose a population function P(t) satisfies the following differential equation. P is measured in millions and t is in years. dP = P(P – 10), dt (a) [5 points] Sketch a slope field. (b) [5 points] Identify the equilibrium solutions (constant solutions) and classify them as stable, unstable, or semi-stable equilibrium. (c) [5 points] Sketch a solution that satisfies the initial condition P(0)= 6. [Show asymptote, if there is one, and indicate the exact P value of the inflection point.] (d) [ 4 points] Write a definite integral for computing the time that it takes for an initial population of 6 (millions) to decline to 0.5 (million.) [Hint: Separate the variables. Think of t as a function of P.]
- Differential Equation 1 (25.12 KiB) Viewed 31 times