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More on Modeling 1.2: Separation of Variables

HW change: 1.2 #38 is not due this week. Bring your CD-ROM to class Tuesday. More on Modeling 1.2: Separation of Variables. January 18, 2007. From last time…. A mystery. Here’s a new population model… Find the equilibrium solutions.

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More on Modeling 1.2: Separation of Variables

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  1. HW change: 1.2 #38 is not due this week. • Bring your CD-ROM to class Tuesday. More on Modeling1.2: Separation of Variables January 18, 2007

  2. From last time… A mystery Here’s a new population model… • Find the equilibrium solutions. • For what values of P is the population increasing? decreasing? • Sketch some solutions to the differential equation. • Can you think of a situation in which this model makes sense? Be creative…

  3. Spread of a rumor(group work) Quantities: (identify as indep var, dep var, or parameter) • P = population of city • N = people who have heard the rumor • t = time • k = proportionality constant Answers: • dN/dt • P - N • dN/dt = k(P - N) • dN/dt = k(350 - N) (N is in thousands, t could be days, weeks, etc. Your choice of units for t affects the value of k.) What should solutions look like? equilibrium solutions?

  4. mmmm… Chocolate! Quantities: • T = temp (degrees F) of hot chocolate at time t • t = time in minutes, hours, etc. (Why doesn’t it matter?) • k = proportionality constant Equation: (Should k be positive or negative?)

  5. HUH????? I asked you to look at the statement on p. 22: “So we should never be wrong.” What does that mean? Check this out: Paul says “y1(t) = 1 + t is a solution.” Glen says “y2(t) = 1 + 2t is a solution.” Bob says “y3(t) = 1 is a solution.” Who is right? How can we tell?

  6. Separable Diffy-Q’s Example: Suppose the chocolate started out at 150o and was 100o 15 minutes later. How would you solve this initial value problem?

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