How many people do you know who’ve been nominated for the Ice Bucket Challenge? Have you yourself been nominated and taped yourself being soaked by a freezing cold bucket of water? Are your kids talking about it?

How about bringing the following question up during your next Dinner Time Maths chat and seeing where it leads?

How many days will it take for all the adults of Australia to be nominated for and take part in the Ice Bucket Challenge fundraiser for ALS?

16 days.

No, I’m not missing a zero and my calculator isn’t broken. Based on a mathematical model, it will take just over 15 days for every adult to be nominated and then dump a bucket of iced water over themselves.

Don’t believe me? Let’s take a look at the maths.

Roughly 80% of Australia’s current population are adults. This gives us about 18 000 000 adults in Australia right now.

Let’s assume that the first day the Ice Bucket Challenge happened in Australia, one person was nominated and taped a video of themselves dumping a bucket of iced water over themselves. They then put the video up on a social media site and nominated 3 others to complete the challenge within 24 hours.

One other significant assumption that we’re making here is that all people accept and follow through on their nomination. In turn, each person nominated goes on and nominates another 3 people who haven’t yet had a go at the challenge.

So on Day 1 we have 1 person.

On Day 2 we have 3 people.

How many people will we have on Day 3?

If each of the 3 people from Day 2 nominate 3 people each, we’ll now have 9 people.

So what’s the pattern here? Each day the number of people taking part is three times the number of people from the day before. This is what we call exponential growth. So let’s watch the numbers take off and reach 18 000 000 in just 16 days!

Day            Number of             Total Number

                    New People          of People

1                1                                 1

2               3                                 4

3               9                                13

4               27                              40

5               81                              121

6               243                          364

7               729                          1 093

8              2 187                       3 280

9              6 561                       9 841

10            19 683                    29 524

11            59 049                    88 573

12            177 147                   265 720

13            531 441                  797 161

14            1 594 323              2 391 484

15            4 782 969             7 174 453

16            14 348 907           21 523 360

How many days did your kids guess? I bet they didn’t believe you when you told them it was only 16 days. But as we can see, with a few simple and fairly realistic assumptions, the mathematical model doesn’t lie!

Exponential growth is powerful. It’s the reason people modelling an Ebola outbreak feel alarmed and why people modelling the advancements of technology are so excited.