The exponential growth of populations can be challenging to comprehend, in part because exponential increases are not as familiar as simple additive increases. In fact, people often grossly underestimate the effect of exponential growth. Consider the following job offer: A corporate executive needs a temporary assistant for a 30-day assignment. The executive proposes to pay you either

(a) $1000/day for 30 days, or

(b) to start at 1 cent per day and then double the salary on each subsequent day (such that you earn 1 cent on the first day, 2 cents on the second day, 4 cents on the third day, 8 cents on the fourth day, and so on). You take the first option, reckoning that

$1000 per day for 30 days is a much better salary than one that starts at 0.001% of that rate and doubles every day for 30 days.

Questions

1. What is the definition of exponential growth?
2. Which salary proposal is an example of exponential growth?
3. What would your earnings be for the month if you choose proposal (a)?
4. What would your earnings be for the 25th day of the month if you choose proposal (b)? (You may need to make a table to calculate this, but you can also use the following equation: daily wage = 2ⁿ, where n = the day.)
5. Reflect on your answers to questions 1–4 above and explain why the statement bolded above sounds right, but isn’t.