Solve the problem.
-For a culture of 30,000 bacteria of a certain strain, the number of bacteria $\mathrm { N }$ that will survive $x$ hours is modeled by the formula $\mathrm { N } = 3000 \sqrt { 100 - \mathrm { x } }$. After how many hours will 27,000 bacteria survive?
A) $19 \mathrm { hr }$
B) $91 \mathrm { hr }$
C) $73 \mathrm { hr }$
D) $81 \mathrm { hr }$

Question

Quizplus · Accepted Answer

To find the number of hours after which 27,000 bacteria will survive, we set $N = 27000$ and solve for $x$:$$27000 = 3000\sqrt{100 - x}$$Dividing both sides by 3000 gives:$$9 = \sqrt{100 - x}$$Squaring both sides gives:$$81 = 100 - x$$Solving for $x$ gives:$$x = 19$$Therefore, after 19 hours, 27,000 bacteria will survive.

Solve the Problem N\mathrm { N }N That Will Survive xxx Hours Is Modeled by the Formula

Solve the Problem $\mathrm { N }$ That Will Survive $x$ Hours Is Modeled by the Formula