Inverse functions

Question

The percentage of material retained during algebra class varies directly as the square of the number of hours of sleep a student got the night before and varies inversely to the number of hours a student parted the previous night. If a student retains 70% of the material after 6 hours of sleep and 2 hours partying, how much material is retained after 8 hours of sleep and 3 hours of partying?

Answer 1

Let M = % of material retained

       n = number of hours of sleep

       p = number of hours partying

 

M varies directly as n² and inversely as p.

 

So, M = kn²/p, for some constant, k.

 

M = 70 when n = 6 and p = 2, so 70 = k(6)²/2

 

                                                          70 = 18k

 

                                                            k = 70/18 = 35/9

 

Therefore, M = 35n²/(9p)

 

When n = 8 and p = 3, M = 35(8)²/27 ≈ 83