For a certain strain of bacteria, the number of bacteria present after t hours is given by the equation Q = Q _oe^{0.34 t}where Q _o represents the initial number of bacteria. How long will it take 400 bacteria to increase to 4,000 bacteria? Express answer to the nearest tenth. A) t = 19.9 hours B) t = 0.3 hours C) t = 6.8 hours D) t = 2.3 hours

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Quizplus · Accepted Answer

We need to solve for t in the equation Q = Q _oe^{0.34 t}, where Q _o is the initial number of bacteria. We know that we want Q to increase from 400 bacteria to 4,000 bacteria. So we can set up the equation: 4,000 = 400 e^(0.34t) Divide both sides by 400: 10 = e^(0.34t) Take the natural logarithm of both sides: ln(10) = 0.34t Solve for t: t = ln(10) / 0.34 Using a calculator, we get t ≈ 6.8 hours. Therefore, the answer is C.

For a Certain Strain of Bacteria, the Number of Bacteria