Question

A production formula for a student's performance on a difficult English examination is given by

g(t, x) = 3tx − 0.1t² − x²,

where g is the grade the student can expect to get, t is the number of hours of study for the examination, and x is the student's grade-point average.

(a) Calculate

g_t(10, 3)

and

g_x(10, 3).

gt(10, 3)	=
gx(10, 3)	=

Interpret the results.

If you have studied for  hours and have a GPA of  , your score on the examination is increasing by  points for each additional hour of study and by  points for each additional point of GPA.

(b) What does the ratio

g_t(10, 3)

g_x(10, 3)

tell about the relative merits of study and grade-point average?

At a level of  hours of study with a GPA of  , one additional hour of study is equivalent to an increase of  (rounded to three decimal places) in GPA (as far as your test score is concerned).

Answer 1