#5 A productivity formula for a student?s performance on a basket-weaving examin

Question

#5

A productivity formula for a student?s performance on a basket-weaving examination is where g is the score the student can expect to obtain, t is the number of hours of study for the examination, and x is the student?s grade-point average. (a) For how long should a student with a 3.0 grade-point average study in order to score 79 on the examination? (Round your answer to two decimal places.) t= hr (b) Find dt/dx for a student who earns a score of 79, evaluate it when x = 3.0. (Round your answer to four decimal places.) Dt/dx = hr per grade point Interpret the result. Note that this is positive, implying that the required study hours Select as the grade point average increases. This means that, for a 3.0 student who scores 79 on the examination, a 1.0 grade point is worth hours more study time. In other words, the higher your GPA, the harder you have to study for the test!

Explanation / Answer

g = 11tx - 0.2t^2 - 10x^2

g --> score

t --> # of hours of study ; t < 10

x --> student's GPA

a)

g = 79 , t = to be found , x = 3

g = 11tx - 0.2t^2 - 10x^2

79 = 33t - 0.2t^2 - 90

0.2t^2 - 33t + 169 = 0

Multiply all over by 5 :

t^2 - 165t + 845 = 0

Solving by quadratic formula :

(165 +/- sqrt((-165)^2 - 4(1)(845)) / 2

(165 +/- sqrt(23845)) / 2

(165 + sqrt(23845)) / 2 and (165 - sqrt(23845)) / 2

t = 159.71 and 5.29

But t < 10

So, t = 5.29 ----> FIRST ANSWER

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g = 11tx - 0.2t^2 - 10x^2

dg/dx = 11t + 11x*(dt/dx) - 0.4t*(dt/dx) - 20x

We already found when g = 79 and x = 3, t = 5.2908684

0 = 11(5.2908684) + 11(3)(dt/dx) - 0.4(5.2908684)(dt/dx) - 60

1.8004476 = 30.88365264 * (dt/dx)

dt/dx = 1.8004476 / 30.88365264

dt/dx = 0.0582977545106854

So, dt/dx = 0.0583 hr per gpa ----> SECOND ANSWER

"Required study hours INCREASES as the gpa increases" ---> NEXT ANSWER

When x = 1 and score, g = 79, we find t = 9.85772

9.85772 - 5.2908684 ---> 4.5668516 ---> NEXT ANSWER

So, here are the answers again :

t = 5.29 hr --> FIRST ANSWER
dt/dx = 0.0583 hr per gpa ----> SECOND ANSWER
INCREASES --> THIRD ANSWER
4.5668516 --> FOURTH ANSWER

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