In a lab experiment, 2200 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 6 hours. How many bacteria would there be after 13 hours, to the nearest whole number?
number = 2200 (2)^(13/6) = 9877.666025
or 9878 to the nearest whole number
start at noon
double at 6 pm
double at 12 midnight
at 1 am you breed another hour how much in that hour would lead to twice as much in 6 hours
x^6 = 2
6 log x= log 2
log x = (1/6) log 2 = 0.05017
x = 1.1225
so
2200 * 2 * 2 * 1.1225 = 9878
To solve this problem, we need to use the exponential growth formula. The formula for exponential growth is given by:
N = N0 * 2^(t/d),
where N is the final number of bacteria, N0 is the initial number of bacteria, t is the time elapsed, and d is the doubling time.
In this case, the initial number of bacteria (N0) is 2200, the time elapsed (t) is 13 hours, and the doubling time (d) is 6 hours.
Now, let's plug in these values into the formula:
N = 2200 * 2^(13/6).
To solve this equation, we need to calculate 2^(13/6).
Using a calculator, we find that 2^(13/6) is approximately 4.443.
Now we can substitute this value back into the formula:
N = 2200 * 4.443.
Multiplying these two values, we find that N is approximately 9774.6.
Rounding this number to the nearest whole number, we have approximately 9775 bacteria after 13 hours.