Question

According to a census taken towards the end of the year 2009, the population of a rural town was found to be 64,000. The census authority also found that the population of this particular town had a growth of 5% per annum. In how many years after 2009 did the population of this town reach 74,088 ?

Answer 1

Population in 2009 (P) = 64,000
Let after n years its population be 74,088(A)
Growth rate= 5% per annum

∴ A = `"P"( 1 + r/100 )^n`

⇒ `(74,088)/(64,000) = (21/20)^n`

⇒ `( 9,261)/(8,000) = ( 21/20)^n`

⇒ `(21/20)^3 = ( 21/20)^n`

On comparing, we get,
n = 3 years