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?

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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?

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Answer 1 · 2016-12-01T07:35:52

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

Explanation:

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

As it started with $500$ $500$ at the end of one week it will be $500 + 500 \times \frac{70}{100} = 500 + 350 = 850$ $500+500xx70/100=500+350=850$ , hence, in one week, it becomes $\frac{850}{500} = 1.7$ $850/500=1.7$ times what it was at the beginning of week i.e. $500 \times 1.7$ $500xx1.7$ .

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

So in second week it will become $850 \times 1.7$ $850xx1.7$ or $500 \times 1.7 \times 1.7$ $500xx1.7xx1.7$ or $500 \times {1.7}^{2}$ $500xx1.7^2$ .

and in $15$ $15$ weeks it will become

$500 \times {1.7}^{15} = 500 \times 2862.4231 ≅ 1431211$ $500xx1.7^15=500xx2862.4231~=1431211$

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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

Explanation:

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