Question

How many objects are required to keep the computer busy for exactly 7 seconds?

Answer 1

48 objects

Explanation:

The number of objects that the computer can sort (x) in t seconds is modeled by the function.

`t=0.003x^2+0.001x`

To determine the number of objects required to keep the computer busy for 7 seconds, we must put
`t=7` into the equation and solve for x.

`7=0.003x^2+0.001x`

This implies that;

`0.003x^2+0.001x-7=0`

or

`3x^2+x-7000=0`

We use the quadratic formula with a=3,b=1,c=-7000

`x=(-b\pm√(b^2-4ac) )/(2a)`

We substitute the values to obtain;

`x=(-1\pm√(1^2-4(3)(-7000)) )/(2(3))`

`x=(-1\pm√(84001) )/(6)`

`x=48.138\:or\:x=-48.472`

We discard value and obtain the number of objects to be 48 to nearest whole object.