Question #1081

Based on the data from a local college, a statistician determined that the average student's GPA at this college is a function of the number of hours, h, he or she studies each week. The grade point average can be estimated by the function"G(h) = 0.006h^2+0.02h+1.2 for 0 is less than or equal to h is less than or equal to 20.
Please provide the steps to find the answer for each question 1,2, and 3! Thank u :)&
1) To the nearest tenth, what is average GPA of a student who doesn't study?&
2) To the nearest tenth, what is the average GPA of a student who studies 12 hours per week?&
3) To the nearest tenth, how many hours of studying are required for the average student to achieve a 3.2 GPA?

Expert's answer

1. The number of hours of a student who doesn't study equals to zero: h=0

G(h=0) = 1.2

2. G(h=12) = 0.006*12^{2}+0.02*12+1.2 = 2.2

3. G(h) = 3.2

0.006h^{2}+0.02h+1.2 = 3.2;

0.006h^{2}+0.02h - 2 = 0;

D = 0.0004 + 0.048 = 0.0484

h = (-0.02 + 0.22)/0.012 = 16.7 hours

G(h=0) = 1.2

2. G(h=12) = 0.006*12

3. G(h) = 3.2

0.006h

0.006h

D = 0.0004 + 0.048 = 0.0484

h = (-0.02 + 0.22)/0.012 = 16.7 hours

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