A culture of bacteria grows exponentially. It doubles in size every 81 hours. How long will it take to triple from its original size?
Answer: hours.
To determine how long it will take for the bacteria culture to triple in size, we need to use the concept of exponential growth.
Given that the bacteria doubles in size every 81 hours, we can express this growth using the equation:
N = N0 * (2^(t/d))
Where:
N0 represents the initial size of the bacteria culture
N represents the size of the bacteria culture after time t
d represents the doubling time (81 hours in this case)
t represents the time period we want to find (in hours)
Since we want to find the time it takes for the bacteria culture to triple from its original size, we can set N = 3 * N0 in the equation:
3 * N0 = N0 * (2^(t/d))
Now, we can simplify the equation:
3 = 2^(t/81)
To solve for t, we need to isolate the exponential term. We can use logarithms to do that. Taking the logarithm (base 2) of both sides gives us:
log₂(3) = (t/81) * log₂(2)
Since log₂(2) is equal to 1, we can simplify the equation further:
log₂(3) = t/81
Now, we can solve for t by isolating it on one side of the equation:
t = 81 * log₂(3)
Using a calculator to evaluate the right-hand side of the equation, we find:
t ≈ 119.12
Therefore, it will take approximately 119.12 hours for the bacteria culture to triple from its original size.