Bacteria colonies can triple in size every 4 days. If you start with 150 bacteria microorganisms, how large would the colony be after 16 days?

Question

Exponential growth equation

Answer 1

On day 0 we have 150 bacteria microorganisms.

Then on day 4, we have 150 x 3 = 450 bacteria microorganisms.

On day 8 we have 450 x 3 = 1350 bacteria microorganisms.

On day 12, there are 1350 x 3 = 4050 bacteria microorganisms.

And finally on day 16, we have 4050 x 3 = 12,150 bacteria microorganisms.

But notice that the colony tripled 4 times in 16 days, or it tripled 16 / 4 = 4 times. So on day 16 our colony size was 150 x 3 x 3 x 3 x 3 = 150 x 3⁴ = 150 x 81 = 12,150. (Looking at the problem this way would be easier if you wanted to know the colony size after, say, 160 days, rather than only 16 days.)