Question

I have a cockroach problem in my living room. Don't ask how, but I counted 125 cockroaches

today. And they are growing at a rate of 20% every day.
How many cockroaches do you think I'll have after three days?

Answer 1

216 cockroaches

Explanation:

Let's establish that 125 cockroahes is Day 0, the start. This means Day 1 is the next day.

Day 0 is 125 cockroaches.

They grow at 20% per day. That is a factor of 120% for the second day.

(125)*(1.20) = 150 cockroaches on Day 1.

The second day would be (150)*(1.20) = 180 cockroaches on Day 2.

The third day is (180)*(1.20) = 216 cockroaches on Day 3.

Let C(x) be the number of cockroaches on the xth day. The resulting formula for this would be:

The third day (x=3)

C(x) = 125*(1.20)^x

C(3) = (1.25)^(1.20)^3