Question

The population of a town three years ago was 'b' and the population of the town three years from now will be 'c'. What is the current population of the town, if it grows at the same rate? (a) √(bc) (b) b√(c) (c) c√(b) (d) b√(b/c) (e) √(b/c)

Answer 1

your correct answer is√bc

Answer 2

Answer:

(a) $\sqrt{(bc)}$

Step-by-step explanation:

Let x bet the current population of the town,

And, r be the rate of increasing per year,

Given,

Initial population of town = b,

⇒ The population after 3 years from starting = x ,

$b(1+\frac{r}{100})^3=x$

$\implies (1+\frac{r}{100})^3=\frac{x}{b}-------(1)$

Also, The population after 6 years from starting = c,

$b(1+\frac{r}{100})^6=c$

$b (\frac{x}{b})^2=c$   ( From equation (1) )

$\frac{x^2}{b}=c$

$x^2=bc\implies x = \sqrt{bc}$

Hence, the current population of town is √(bc).