Question

The number of bacteria in a certain sample increases according to the following function, where y0 is the initial number present, and y is the number present at t (in hours).y=y0e^0.067tHow many hours does it take for the size of the samples to double. Do not round any intermediate computations, and round your answer to the nearest tenths.

Answer 1

Answer: 10.3

Given:

$y=y_0e^{0.067t}$

We are to find how many hours would it take for the size of the samples to double. Given that y is the number present at t hours, we know that we need to find how long would it take for y = 2y0.

We can now solve this by substituting y = 2y0

$y=y_0e^{0.067t}$$2y_0=y_0e^{0.067t}$

*cancel out y0

$2=e^{0.067t}$

*solve for t

$\ln 2=0.067t$$t=\frac{\ln 2}{0.067}$$t=10.345\approx10.3$

Therefore, at 10.3 hours, the sample will double in size.