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) = 50/412t 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/(412t). 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.