6-3 More Difficult Separation of Variables Rizzi – Calc BC

Return of Separation of Variables

Practice with Separable Diff Eq

Particular Solutions

One More…

Application – Populations

Answer  When t = 3, you can approximate the population to be N = 650 – 350e –0.4236(3) ≈ 552 coyotes.

Logistic Differential Equations – BC Topic Rizzi – Calc BC

Recap  Yesterday, we looked at the coyote problem and came up with the following equations to describe the coyote population: Differential EquationSolution to Diff Eq

The Logistic Equation  Exponential growth is unlimited, but when describing a population, there often exists some upper limit L past which growth cannot occur. This upper limit L is called the carrying capacity, which is the maximum population y(t) that can be sustained or supported as time t increases.

What do you see in this slope field?

General Solution  Given the logistic differential equation  The general solution is

Nuances  Population __________

Practice

AP Style Question