Suppose a population of bacteria in a Petri dish has a doubling time of 6 hours. How long will it take for an initial population of 11000 bacteria to reach 20500? Round your answer to two decimal places.
To find the time it will take for the population to reach 20500 bacteria, we can use the formula for exponential growth:
N = N0 * 2^(t/d)
where:
N is the final population size (20500 bacteria),
N0 is the initial population size (11000 bacteria),
t is the time it takes for the population to reach N (which we want to find), and
d is the doubling time (6 hours).
Rearranging the formula to solve for t, we have:
t = d * log2(N/N0)
Plugging in the values we know:
t = 6 * log2(20500/11000)
To calculate log2(20500/11000), we can use a calculator or software with logarithmic functions, such as Excel or a scientific calculator. The result is approximately 0.786.
Now, substitute this value back into the equation:
t = 6 * 0.786
Calculating 6 * 0.786, we find that it will take approximately 4.716 hours for the population to reach 20500 bacteria.
Rounding this to two decimal places, the answer is 4.72 hours.
20.5/11 = 2^n
n log 2 = log 1.8636
n = .898
.898 * 6 hours = 5.39 hours