Linear growth and exponential growth

For a question you've never met, the book suggests a method. First, guess: quickly, by instinct, no working. Then calculate: say how the quantities you need are related, make sensible assumptions for anything you don't know, work it out, and see how close your guess was. 'Initially, your guesses may be very far off from the answer and it is perfectly fine!'

An example. Nanjundappa wants to donate jaggery equal to Roxie's weight and wheat equal to Estu's. What are they worth?

The practice is real and old. 'Tulābhāra or Tulābhāram, the practice of offering goods equal to the weight of a person, is quite old and is still followed in many places in Southern India. It is a symbol of bhakti (surrendering oneself), a token of gratitude; it also supports the community.' Roxie then wonders: how many 1-rupee coins would equal her weight? Guess first (hundreds? thousands? lakhs?), then weigh a coin and find out.

Another: Roxie and Estu hear someone say they walked about 400 km to reach a place. How long ago did they set out? Pādayātra is 'the traditional practice of walking long distances as part of a religious or spiritual pursuit', followed across religions here under many names: Ajmer Sharif Dargah Ziyarat, Pandharpur Wari, Kānwar Yatra, Sabarimala Yatra, Sammed Shikharji Yatra, Lumbini to Sarnath Yatra.

Now the chapter's real point. Roxie is reading a novel in which a ladder is built to the Moon, and wonders how many steps it would need. Take the steps 20 cm apart and the Moon 3,84,400 km away.

The answer is 1,92,20,00,000 steps: 192 crore 20 lakh of them (about 1.9 billion). Each step adds a fixed 20 cm, and that's called linear growth.

Side by side:

Linear growth is additive, whereas exponential growth is multiplicative, and that one word is the whole difference.