Answer: 1/16,384 microbes
Step-by-step explanation:
Since the microbes divides every 30minutes, if the microbes divides by half every 30minutes, then after an hour it will divides by another half that is (1/2)of 1/2 to give 1/4.
Subsequently after another hour, the microbes will reduces to 1/4 of its remains (i.e 1/4) to give 1/16.
Since the denominator is increasing geometrically each hour.
Looking at the trend;
After 1hr = 1/4 of the original microbe = 1/4
After 2 hrs = 1/4 of the remaining microbe = 1/4 of 1/4 = 1/16
Generalizing, we will let the number of hours be n
According to the progression, 1, 1/4,1/16,...n
Since its a Geometric Progression, nth term = ar^n-1
Where a is the first term = 1
r is the common ratio = 1/4
n is the number of hours of decay
After 8hours, the microbes will have been divided by
(1)(1/4)^8-1
= (1/4)^7
= 1/16,384 microbes
