Question

A study found that a​ student's GPA,​ g, is related to the number of hours worked each​ week, h, by the equation g=-0.0007h^2+0.015h+3.03. Estimate the number of hours worked each week for a student with a GPA of 2.15.

Answer 1

Answer:

A student with GPA of 2.15 worked 47.8 hours per week.

Step-by-step explanation:

To find the numbers of hours worked when the GPA is 2.15, we solve the equation when $g=2.15$ or:

$2.15= -0.0007h^2+0.015h+3.03$

which can be rewritten as (by subtracting 2.15 from both sides)

$-0.0007h^2+0.015h+0.88=0$.

We solve this using the quadratic equation which says, for $ax^2+bx+c=0$,

$x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

in our case

$a=-0.0007$

$b=0.015$,

therefore, we have

$x=\frac{-0.015\pm\sqrt{0.015^2-4(-0.0007)(0.88)} }{2((-0.0007) }$

$x=\frac{-0.015\pm0.051856 }{-0.0014 }$

$\boxed{x=47.8}\\\\ \boxed{x =-26.3}$

and since only the positive solution applies to the real word, we choose $x=47.8$, and therefore, a student with GPA of 2.15 worked 47.8 hours per week.