Question

During what time interval should the camera be turned on in order to preserve battery power when the camera is too distant to be used. (College precalc- nonlinear inequalities).

Answer 1

From the given equation we get that the optimal time is represented by the following inequality:

$|100t-1200|\le200.$

Now, recall that:

$\begin{gathered} |a|\leq b\text{ if and only if } \\ -b\leq a\leq b\text{.} \end{gathered}$

Therefore:

$-200\le100t-1200\le200.$

adding 1200 to the above inequality, we get:

$1000\le100t\le1400.$

Finally, dividing by 100 we get:

$10\le t\le14.$

Answer: The time interval is between 10 and 14 days.