neil was growing a culture of bacteria for a biology experiment. he noticed that the population doubled after 90 minutes. if the population grows exponentially, how many times the original population will there be after six hours?
Looks like base 2 numerals:
90min. = 1.5h,
6h / 1.5h = 4.
Po = 2^0 = 1 = Initial pop.
P = 2^4 = 16 times Po.
To determine the number of times the original population will double after six hours, we need to convert the time to the same unit as the doubling time.
Given that the population doubles every 90 minutes, we can calculate the number of doubling periods in six hours.
Since there are 60 minutes in an hour, the number of minutes in six hours is:
6 hours * 60 minutes/hour = 360 minutes
Next, we divide the total time (360 minutes) by the doubling time (90 minutes) to find the number of doubling periods:
Number of doubling periods = 360 minutes / 90 minutes = 4 doubling periods
So, the original population will double four times in six hours.
Since each doubling multiplies the population by 2, the final population will be:
2^4 = 16 times the original population
Therefore, after six hours, there will be 16 times the original population.