Chapter - 5 task question - XP Math - Forums

 XP Math - Forums Chapter - 5 task question

 03-28-2010 #1 magmagod   Join Date: Mar 2010 Posts: 9 Chapter - 5 task question Researchers at a school board have developed models to predict the population changes in the three areas they service. The models are A(t) = 360/t+6 for area A, B(t) = 30t/t+1 for B, and C(t) = 50/41-2t for area C, where the population is measured in thousands and t is the time in years since 2007. The existing schools are full and the board has agreed that a new school should be built. I have done the first 4 questions asking to graph and state the intervals of increase and decrease (i used an interval chart)... but the last question asks this: Determine when the population of area B will be increasing most rapidly and when the population of area C will be increasing most rapidly. How would you solve this? would you just solve the innequality of each area greater than zero and then do the interval chart...or figure it out from the graph? please help
 03-29-2010 #2 jmw106462     Join Date: Feb 2010 Posts: 388 I Don't know the answer to that problem people at Mathacademy might? __________________ Please refrain from sending me frivolous PM's
 03-29-2010 #3 magmagod   Join Date: Mar 2010 Posts: 9 People at who??
03-31-2010   #4
MAS1

Join Date: Dec 2008
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Quote:
 Originally Posted by magmagod Researchers at a school board have developed models to predict the population changes in the three areas they service. The models are A(t) = 360/t+6 for area A, B(t) = 30t/t+1 for B, and C(t) = 50/41-2t for area C, where the population is measured in thousands and t is the time in years since 2007. The existing schools are full and the board has agreed that a new school should be built. I have done the first 4 questions asking to graph and state the intervals of increase and decrease (i used an interval chart)... but the last question asks this: Determine when the population of area B will be increasing most rapidly and when the population of area C will be increasing most rapidly. How would you solve this? would you just solve the innequality of each area greater than zero and then do the interval chart...or figure it out from the graph? please help
If I understand the models correctly then A(t) = 360/(t+6), B(t) = 30t/(t+1), and C(t) = 50/(41-2t). The only one of the three which is increasing is B(t) and its fastest increase comes in the 1st year. If 2007 is t = 0 and 2008 is t = 1, then B(0) = 0 and B(1) = 15. The increases start to level off and approaches 30 as t goes to infinity. A(t) and C(t) are always decreasing functions. The graph shows these features very well.

 03-31-2010 #5 shadow123blast     Join Date: Feb 2010 Posts: 117 answer For B it would be when t=0 since it jumps from 0 to 15 For a i guess it would be from 0 too since you can only use positive days and that was the least.
 03-31-2010 #6 shadow123blast     Join Date: Feb 2010 Posts: 117 oh yeah go to the art of problem solving register and ask on the forums and lots of excellent math people will come and answer (but there already are)
 04-01-2010 #7 jmw106462     Join Date: Feb 2010 Posts: 388 I don't like Artofproblemsolving.com They well can't say __________________ Please refrain from sending me frivolous PM's

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