How does a single infection become a full-blown pandemic, leading to a shortage of hospital beds and thousands of deaths? The answer is exponential growth, and it's time to talk about it.
Suppose a mysterious new virus has entered the city of Zeta. And unluckily, Adam becomes the city's first person to catch the virus. Now, this virus spreads from only a newly infected person, and can infect only two other people.
Should we be scared? Let's take a look at how the virus spreads for the first three days:
Adam spreads the virus to two other people. So, the number of newly infected people at the end of the day would be 1 x 2 or 2.
The two newly infected people from day 1 spread it to two more people, each taking the tally of new infections to 4 (i.e. 2 x 2).
The four people from day 2 spread it further to two people each. At the end of Day 3, we have 8 (i.e. 4 x 2) new infected people.
Ok, so 2 became 4, and that doubled to 8. Seems like a harmless spread, right?
Wrong! Work out how many infected people would be there at the end of the 20th day, and you’d realize why the city of Zeta would face hospital bed shortages and be full of snaking lines outside its pharmacies.
For those who are still working out the answer, it’s over a million (2²⁰)! By repeatedly doubling, 2 became 4, then 8, then 16, 32, 64, 128, 256, …, 524288, and finally 1048576! Notice how harmless the jump from 2 to 4 looks, but on the 20th day, the jump is more than half a million!
This kind of growth, i.e. when we multiply a number with another number (greater than 1) repeatedly, is known as exponential growth.
And exponential growth is fast. Really fast! Just to give you an idea of how crazy it is, here’s a little simulation.
Drag the slider to the right to see how quickly the product increases with n, i.e. the number of 2s multipled. At n = 20, the product crosses a million. And, at n = 30, it crosses a billion!
And what if each infected person was able to infect three other people? Here’s another simulation which demonstrates that.
Can you find the number of newly infected people at the end of two weeks? Three weeks? A month?
Hope that you now understand the power of exponential growth, and realize that it shouldn't been taken lightly.
But can we save the city of Zeta? We'll discuss that in another article. Stay tuned!