If bacteria doubles every 20 minutes, how long until you have a billion spores
To calculate the time it takes for bacteria to double and reach a billion spores, we can use the concept of exponential growth.
If bacteria doubles every 20 minutes, it means that the growth rate is constant. We can express this growth as an exponential function:
N(t) = N0 * 2^(t/d)
Where:
N(t) is the final number of spores at time t
N0 is the initial number of spores
t is the time in minutes
d is the doubling time in minutes
In this case, we want to find the time it takes for the number of spores to reach a billion, which is 10^9.
N(t) = 10^9
N0 = 1 (since we start with one spore, given in the question)
d = 20 minutes (the doubling time)
Substituting these values into our equation:
10^9 = 1 * 2^(t/20)
To find the value of t, we need to solve this equation for t. Taking the logarithm of both sides can help us isolate t:
log(10^9) = log(2^(t/20))
9 = (t/20) * log(2)
Now we can solve for t by rearranging the equation:
t = 20 * (9 / log(2))
Using a scientific calculator, we find:
t ≈ 138.63 minutes
Therefore, it would take approximately 138.63 minutes for the number of bacteria to reach a billion spores, given that they double every 20 minutes.