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2013 Math Kangaroo

Problem 6

Problem 6 · 2013 Math Kangaroo Medium
Algebra & Patterns substitution

Let f be a linear function for which \(f(2013) - f(2001) = 100\). What is the value of \(f(2031) - f(2013)\)?

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Answer: D — 150
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Hint 1 of 2
A linear function changes by the same amount over equal steps.
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Hint 2 of 2
Find the per-year change, then scale it to the new gap.
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Approach: constant slope of a linear function
  1. From 2001 to 2013 is 12 years and the change is 100, so the slope is 100/12.
  2. From 2013 to 2031 is 18 years.
  3. Change = 18 · (100/12) = 150, so D.
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