Question

A computer can sort x objects in t seconds, as modeled by the function below: t=0.003.12 +0.0013 How many objects are required to keep the computer busy for exactly 7 seconds? Round to the nearest whole object.

Answer 1

`\begin{gathered} t=0.003x^2+0.001x \\ \text{Evaluate the function for t=7} \\ 7=0.003x^2+0.001x \\ \text{ Rewrite the equation as:} \\ 0.003x^2+0.001x-7=0 \end{gathered}`

The solutions are:

`\begin{gathered} x=48.13821001 \\ or \\ x=-48.47154335 \\ \text{Let's take the positive solution, } \\ x\approx48 \end{gathered}`

Quadratic formula:

`\begin{gathered} \text{Given a equation:} \\ ax^2+bx+c=0 \\ \text{The solutions for this equation can be found using this formula:} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ In\text{ the previous problem:} \\ a=0.003 \\ b=0.001 \\ c=-7 \end{gathered}`