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Calculus!

Calculus!. By: Drew Lewis. Law of Exponential Change. Table of Contents. Consider the Equation Step 1: Separate the Variables Step 2: Integrate Step 3: Solve for y Step 4: Find y(0 ) Law of Exponential Change. Consider the Equation…. dy /dx= ky k is a constant

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Calculus!

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  1. Calculus! By: Drew Lewis Law of Exponential Change

  2. Table of Contents • Consider the Equation • Step 1: Separate the Variables • Step 2: Integrate • Step 3: Solve for y • Step 4: Find y(0) • Law of Exponential Change

  3. Consider the Equation… • dy/dx=ky • k is a constant • The rate of change of y is proportional to the amount present. • Goal: Solve dy/dx=ky for y…

  4. Step 1: Separate the Variables dy/dx=ky (1/y)dy=(k)dx *If you don’t separate variables, you get no credit on the AP exam.

  5. Step 2: Integrate ∫(1/y)dy= ∫ (k)dx ln|y|=kx + C *If you forget “+C” then you will get no credit on the AP exam.

  6. Step 3: Solve for y ln|y|=kx + C e^lny=e^(kx +C) y=(C)e^(kx)

  7. Step 4: Find y(0) y=(C)e^kx y(0)=(C)e^0 y(0)=C • Therefore…

  8. Law of Exponential Change • y=y(0)e^(kx) • If dy/dx=ky, then y=y(0)e^kx • For more help on the Law of Exponential Change and practice problems, check out: http://saylor.org/site/wp-content/uploads/2012/09/MA102-6.4.5-Growth-and-Decay.pdf

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