The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of
3.9%
per hour. How many hours does it take for the size of the sample to double?
What is the School Subject? If you want help with your homework, this question seems not to require a social studies or English tutor. Is this biology, math, or what is your subject?
it will take t hours, where
1.039^t = 2
and if you are unfamiliar with log equations, take the log of each side..
t*log1.039=log2
t= log(2)/log(1.030
and put this into your google search window
log(2)/log(1.030) =
and it is about 23 hours...
To find the number of hours it takes for the size of the sample to double, we can use the formula for exponential growth:
N(t) = N0 * e^(rt)
Where:
N(t) is the size of the sample at time t
N0 is the initial size of the sample
e is the base of the natural logarithm (approximately 2.71828)
r is the growth rate parameter
t is the time in hours
In this case, we want to find the value of t when N(t) = 2 * N0. So we can set up the equation:
2 * N0 = N0 * e^(rt)
Dividing both sides by N0 gives:
2 = e^(rt)
Taking the natural logarithm of both sides:
ln(2) = rt
Now we can solve for t by dividing both sides by r and plugging in the growth rate parameter, which is 3.9% per hour:
t = ln(2) / 0.039
Using a calculator, we can find that ln(2) is approximately 0.69314. Plugging this value into the formula:
t = 0.69314 / 0.039
Simplifying gives:
t ≈ 17.7564 hours
Therefore, it takes approximately 17.76 hours for the size of the sample to double.