August 19th, 2011, 08:05 AM  #1 
Member Joined: Aug 2011 From: Alabama Posts: 93 Thanks: 0  Relation?
What is the relation of these values? I can't figure it out. For a child between the ages of 6 and 16, its height y (in inches) is approximately a linear function of age t (in years). Joe Smith’s son John was 40 inches tall at age 6 and 58 inches tall at age 10. Estimate John’s height at age 15. 
August 19th, 2011, 08:43 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Relation?
You are told essentially that: y(t) = mt + b For John, you are given: y(6) = 40 y(10) = 58 This results in the linear system: (1) 6m + b = 40 (2) 10m + b = 58 Subtracting (1) from (2) we find: 4m = 18 m = 18/4 = 9/2 6(9/2) + b = 40 b = 13 Thus, for John, we have: y(t) = (9/2)t + 13 To estimate John's height at age 15, we use: y(15) = (9/2)15 + 13 = 80.5 
August 19th, 2011, 09:06 AM  #3 
Member Joined: Aug 2011 From: Alabama Posts: 93 Thanks: 0  Re: Relation?
You're seriously a big help. Thanks!

August 21st, 2011, 12:18 PM  #4 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Relation?
As m = 9/2 is determined, like [color=#00FF00]MarkFL[/color] / you did, John grows for 5 more years after his tenth. So his length is estimated at (58 + 5 * 9/2) inches = 80.5 inches.


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