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Section 4.6 Related Rates

Section 4.6 Related Rates. Spreading Like Wildfire!. A circular patch of forest is en fuego . When the radius is 80m, the fire spreads at a rate of 1000 square meters / minute. How quickly is the radius of the blaze growing at that moment?. 1. Organize Information. Identify what you know

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Section 4.6 Related Rates

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  1. Section 4.6Related Rates

  2. Spreading Like Wildfire! A circular patch of forest is en fuego. When the radius is 80m, the fire spreads at a rate of 1000 square meters / minute. How quickly is the radius of the blaze growing at that moment?

  3. 1. Organize Information • Identify what you know • r = 80 • dA/dt = 1000 (notice this is a rate of change) • Identify & Label what you’re trying to find • dr/dt = ??? • We will always be solving for another (related) rate

  4. 2. Write an equation • Must relate all variables whose rates we know or want to find • No derivatives yet!!! • No substituting yet!!!

  5. 3. Differentiate • Always differentiate with respect to time, t. • Remember to use the Chain Rule!! • dA/dt = 2πr dr/dt

  6. Solve • Plug in the numbers you know • dA/dt = 2π r dr/dt • 1000 = 2π (80) dr/dt • Solve for the unknown rate • Dr/dt = 1000/(160 π) ≈ 1.989 meters / min • The radius of the forest fire is increasing at 1.989 meters per minute. • Remember to include proper units

  7. Summary • Organize information • Write an equation that relates known and unknown variables • Differentiate with respect to t • Plug in #’s and solve

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