the population is any place become double in70 years What will be the rate of population growth - Maths - Linear Equations in One Variable

Question

the population is any place become double in70 years What will
be the rate of population growth?

Varun.Rawat · Accepted Answer

let the initial population = P

Rate of growth = R%

Time, n = 70 years

population after 70 years , A = 2P

$n o w, A = P {[1 + \frac{R}{100}]}^{n} \Rightarrow 2 P = P {[1 + \frac{R}{100}]}^{70} \Rightarrow 2 = {[\frac{100 + R}{100}]}^{70} \Rightarrow 2 \times 100^{70} = {[100 + R]}^{70}$

Taking 70^throot both sides, we get

$2^{1 / 70} \times 100 = 100 + R \Rightarrow R = 100 [2^{1 / 70} - 1] %$

the population is any place become double in70 years.What will be the rate of population growth?