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differential equation
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differential equation
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.]
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.]
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