Question

In a biogas plant, the population of yeast bacteria increases at a rate of 9% per annum, but there is an additional annual increase of 1% in population due to various other inputs in the system. The percentage increase in the yeast population after 2yr is:
A. 20%
B. 21%
C. 25%
D. 22%

Answer 1

B. 21%

Step-by-step explanation:

In a biogas plant, the population of a yeast bacteria increases 9% per year.

There is an additional increase of 1% due to various factors.

So total increase in yeast population = 10%

Let's assume X as the current yeast population, so population at the end of one year =  

= (x + 10% of x)

= 1.10x

Population at the end of two years = 1.1x + 10% of1.1x = 1.21x

We find that the population growth forms a geometric sequence in the form of x, x(1.10), x(1.1)²..........

Percentage increase in population after 2 years

= 1.1^2x - x / x  * 100

= 1.21 - 1 * 100

= 21%