# 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?

Dec 1, 2016

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 $500 + 500 \times \frac{70}{100} = 500 + 350 = 850$, hence, in one week, it becomes $\frac{850}{500} = 1.7$ times what it was at the beginning of week i.e. $500 \times 1.7$.

hence, in one week, it becomes $\frac{850}{500} = 1.7$ times what it was at the beginning of week.

So in second week it will become $850 \times 1.7$ or $500 \times 1.7 \times 1.7$ or $500 \times {1.7}^{2}$.

and in $15$ weeks it will become

$500 \times {1.7}^{15} = 500 \times 2862.4231 \cong 1431211$