Question

An employment research company estimates that the value of a recent MBA graduate to an accounting company is

V = 4e2 + 4g3

where V is the value of the graduate, e is the number of years of prior business experience, and g is the graduate school grade point average. A company that currently employs graduates with a 2.9 average wishes to maintain a constant employee value of V = 300, but finds that the grade point average of its new employees is dropping at a rate of 0.4 per year. How fast must the experience of its new employees be growing in order to compensate for the decline in grade point average? (Give the answer to two decimal places.)

Answer 1

(de/dt) = 0.70929

Explanation:

Given

V = 4*e² + 4*g³

where

• V is the value of the graduate

• e is the number of years of prior business experience
• g is the graduate school grade point average

If V = 300 (constant)

g = 2.9

dg/dt = - 0.4

de/dt = ?

we have to get e as follows

V = 4*e² + 4*g³ ⇒ (V/4) = e² + g³ ⇒ e = √((V/4) - g³)

⇒ e = √((300/4) - (2.9)³)

⇒ e = 7.1141

Then we apply

dV/dt = d(4*e² + 4*g³)/dt

d(300)/dt = 4*((2*e*de/dt) + 3*g²*(dg/dt))

0 = (2*e*de/dt) + 3*g²*(dg/dt)

⇒ 0 = 2*(7.1141)*(de/dt) + 3*(2.9)²*(- 0.4)

⇒ (de/dt) = 0.70929