Solve.
-The profit made when $t$ units are sold is given by $P = t ^ { 2 } - 24 t + 140$ for $t > 0$ . Determine the values of $t$ for which $P < 0$ (a loss is taken) .

Question

Solve.
-The profit made when $t$ units are sold is given by $P = t ^ { 2 } - 24 t + 140$ for $t > 0$. Determine the values of $t$ for which $P < 0$ (a loss is taken).
A) $( 10,14 )$
B) $( 0 , \infty )$
C) $[ 10,14 ]$
D) $( - \infty , 10 ) \cup ( 14 , \infty )$

Quizplus · Accepted Answer

To determine the values of $t$ for which $P < 0$, we first need to find the roots of the quadratic equation $P = t^2 - 24t + 140$. Factoring or using the quadratic formula, we find the roots to be $t = 10$ and $t = 14$. Since $P$ is a parabola opening upwards (coefficient of $t^2$ is positive), $P < 0$ between the roots. Therefore, the values of $t$ for which a loss is taken are in the interval $(10, 14)$.

Solve -The Profit Made When ttt Units Are Sold Is Given By

Solve
-The Profit Made When $t$ Units Are Sold Is Given By