Apopulation is growing at 5% a year. how long will it take for this population to double?

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!