Linear Growth vs Exponential Growth (Ladder Example)

Transcript

Linear Growth vs Exponential Growth (Ladder Example)Roxie tells Estu about a science-fiction novel she is reading where they build a ladder to reach the moon, “... I wonder if we actually had a ladder like that, how many steps would it have?”. What do you think? Make an instinctive guess first. Would the number of steps be in thousands, lakhs, crores, or even more? In such type of questions, we need to make necessary and reasonable assumptions for the unknowns and find the answers. To find out, we would need to know the gap between consecutive steps of the ladder. Let’s assume a reasonable distance of 20 cm. Visualising the problem as shown, If we calculate the value, we get the result as 1,92,20,00,000 steps, which is 192 crore and 20 lakh steps or 1 billion 922 million steps. The fixed increase in the distance from the earth with each step (a 20 cm gain after each step) is called linear growth. To cover the distance between the Earth and the Moon, it takes 1,92,20,00,000 steps with linear growth whereas it takes just 46 folds of a piece of paper with exponential growth! Linear growth is additive, whereas exponential growth is multiplicative.