If 40% of villages in a state had internet connectivity in 2015 and this increased to 70% by 2021, what is the average annual growth rate (CAGR) of internet connectivity?

hard 3 marks Class 7 · Geography · Human Environment - Settlement, Transport and Communication

Answer

9.8%

The correct answer is 9.8% — Answer: 9.8%.

Step-by-step solution

Let initial connectivity I0 = 0.40, final I1 = 0.70, number of years n = 2021-2015 = 6.
Use CAGR formula: (I1/I0)^(1/n) - 1.
Compute I1/I0 = 0.70 / 0.40 = 1.75.
Take sixth root: 1.75^(1/6). Use natural logs: ln(1.75)=0.5596, divide by 6 = 0.09327.
Exponentiate: e^(0.09327) ≈ 1.0978.
Subtract 1: 0.0978 ≈ 9.78%.
Round to one decimal place: 9.8%.
Answer: 9.8%.

Common mistake: Subtracting 40% from 70% instead of computing compound growth

Concept tested: CAGR calculation