Exponential Growth
A J-curve graph represents exponential growth. The idea is that populations double slowly while the
numbers are small but once they are large doubling happens quickly. Starting with a small number and
doubling it over and over soon means you are doubling ever-larger numbers.
There are three riddles below to help illustrate the concept of exponential growth, a constant rate of growth
to an ever-increasing base.
Answer each riddle completely and show your thinking.
1. A father complained that his son’s allowance of $5 per week was too much. The son replied, “Okay,
Dad. How about this? You give me one penny for the first day of the month, 2 cents for the second day,
4 cents for the next, 8 cents for the next, and so on for every day of the month.” The father readily
consented.
a. Who was more clever?
b. What would the son’s allowance be on day 30?
c. What would his allowance be during months that have 31 days?
2. Lilly pads have started to grow in a 40-acre pond. The pads double in size each day and will take 40
days to cover the entire pond. On which day will the pads cover exactly half of the pond?
3. A courtier presented the Persian king with a beautiful, hand-made chessboard. The king asked what he
would like in return for his gift and the courtier surprised the king by asking for one grain of rice on the
first square, two grains on the second, four grains on the third etc. The king readily agreed and asked for
the rice to be brought.
(conversion factor: there are approximately 29,000 grains per pound for standard long grain rice)
a. How much rice did the courtier receive?
b. How many pounds of rice does this equal?
Debrief:
1. What have you discovered about exponential growth?
2. How does this relate to human populations?