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?

1 Answer
Dec 1, 2016

Answer:

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#