During 1 st year population would be x
During 2nd year population would be x+(0.05)x
During 3rd year population would be x+2(0.05)x
And so on till the time the term becomes 2x ( as it is said that population doubles)
This means the second term in the above expressions should become equal to x when the population will get double
So let's generalize the second term ( like in x+ 2(0.05)x the second term is 2(0.05)x )
It can be written as
N(0.05) x
Since we want it to be equal to x
Thus,
N(0.05)x = x
N= 20
Now the year which corresponds to N is one more than N ie (N+1)
*So , it would take 21 years to double the population*
Hope it helps!