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

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

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=(-b\pm√(b^2-4ac) )/(2a)`

in our case

`a=-0.0007`

`b=0.015`,

therefore, we have

`x=(-0.015\pm√(0.015^2-4(-0.0007)(0.88)) )/(2((-0.0007) )`

`x=(-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.