Question

The number of bacteria in a certain sample increases according to the following function, where x is the initial number present, and y is the number present at time t (in hours). How many hours does it take for the size of the sample to double? Do not round any intermediate computations, and round your answer to the nearest tenth. y=xe^0.0789t

Answer 1

To find the number of hours it takes for the size of the sample to double, solve the equation y = xe^(0.0789t), where y is the number present at time t and x is the initial number present. t is approximately 8.8 hours when rounded to the nearest tenth.

Step-by-step explanation:

To find the number of hours it takes for the size of the sample to double, we need to solve for t in the equation y = xe^(0.0789t), where y is the number present at time t and x is the initial number present.

1. Let's set y equal to 2x to represent the doubling of the sample size.
2. 2x = xe^(0.0789t)
3. Divide both sides by x: 2 = e^(0.0789t)
4. Take the natural logarithm of both sides: ln(2) = 0.0789t
5. Divide both sides by 0.0789: t = ln(2) / 0.0789

Using a calculator, t is approximately 8.8 hours when rounded to the nearest tenth.