Question

A population of 500 beetles is expected to grow at a rate of 70% per week. Which number is the best prediction of the population after 15 weeks?

Answer 1

The best prediction of the population after 15 weeks is `1431211`

Explanation:

As the population of `500` beetles is expected to grow at a rate of `70%` per week, every week it grows by `70%` of previous week.

As it started with `500` at the end of one week it will be `500+500xx70/100=500+350=850`, hence, in one week, it becomes `850/500=1.7` times what it was at the beginning of week i.e. `500xx1.7`.

hence, in one week, it becomes `850/500=1.7` times what it was at the beginning of week.

So in second week it will become `850xx1.7` or `500xx1.7xx1.7` or `500xx1.7^2`.

and in `15` weeks it will become

`500xx1.7^15=500xx2862.4231~=1431211`