Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

This was a GRE multiple choice question.

At a $15$ percent annual inflation rate, the dollar would decrease by approximately one-half every $5$ years. At this inflation rate, in approximately how many years would the dollar be worth $\dfrac{1}{1,000,000}$ of its present value?

(A) $25$

(B) $50$

(C) $75$

(D) $100$

(E) $125$

The correct answer is (D), and I solved this by running through powers of $2$ and noting $2^{20}\approx 1,000,000$, so it would take around $20\cdot 5=100$ years. Is there a less haphazard way of setting this problem up to solve it?

share|improve this question

2 Answers 2

up vote 3 down vote accepted

The explicit way is to say you want $(\frac 12)^n \lt \frac 1{1000000}, 2^n \gt 1000000$ and take the base 2 log of both sides, getting $n \gt \log_2 1000000=6(\log_2 10) \approx 19.9316$ so $n=20$ is the lowest integer.

A less formal way is to notice that $2^{10}=1024 \gt 1000$ so $2^{20} \gt 10^6$

share|improve this answer

$2^{10} = 1024$ and $1024^2 \approx 1,000,000$ and so, you get $2^{20}$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.