Section 4.6 Related Rates

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Section 4.6Related Rates
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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?
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1. Organize Information

• Identify what you know
• r 80
• dA/dt 1000 (notice this is a rate of change)
• Identify Label what youre trying to find
• dr/dt ???
• We will always be solving for another (related)
  rate

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2. Write an equation

• Must relate all variables whose rates we know or
  want to find
• No derivatives yet!!!
• No substituting yet!!!

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3. Differentiate

• Always differentiate with respect to time, t.
• Remember to use the Chain Rule!!
• dA/dt 2pr dr/dt

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Solve

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

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Summary

1. Organize information
2. Write an equation that relates known and unknown
   variables
3. Differentiate with respect to t
4. Plug in s and solve