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In Simple Terms

Annie and Ben are both doing the question...

A 100m cliff erodes by 2/7 of its height each year.

(a) What will the height of the cliff be after 10 years?

Annie believes the answer is 100*(5/7)^9 because using the geometric progression formula exactly is common sense.

Ben believes the answer is 100*(5/7)^10 because it's 10 years later.

In your answer, determine whether Annie is right or wrong, giving reasons. Also determine whether Ben is right or wrong, also giving reasons.

The Actual Question

An extension to this question.

Can the question...

A 100m cliff erodes by 2/7 of its height each year.

(a) What will the height of the cliff be after 10 years?

...Be interpreted in different ways so that you could answer like this:

 100*(5/7)^10
=976562500/282475249
=3.46m to 2d.p.

Or this:

 100*(5/7)^9
=195312500/40353607
=4.84m to 2d.p.

I tried to convince my teacher that his answer wasn't correct but he said that his answer was an interpretation. The answer made in this previous question supported my answer, but my teacher still thinks he is right.

Can you really interpret this question in the 2 ways above or is there only just one right and the rest wrong? (Excluding the simplification of answers. Also some other questions are designed to have more than one answer.)

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  • $\begingroup$ You have already received multiple responses in your "previous question" explaining everything in detail. Creating a duplicate post is both unnecessary and a breach of community guidelines. $\endgroup$
    – heropup
    May 5, 2016 at 6:29
  • $\begingroup$ Although it is indeed very similar to my last question, I'm still not sure whether the other option is correct and valid as an 'interpretation'. Maybe I should say whether this question has more than 1 answer. $\endgroup$
    – Bradman175
    May 5, 2016 at 6:37
  • $\begingroup$ Have you received any responses to your questions on this site that would give you even the slightest impression that there exists more than one valid interpretation of the problem, and that there exists more than one valid numeric answer? No. So why do you keep asking for an alternative interpretation that does not exist? $\endgroup$
    – heropup
    May 5, 2016 at 6:47
  • $\begingroup$ OP is clearly just pandering for someone to tell them that they're right about something they're clearly not. $\endgroup$
    – MT_
    May 5, 2016 at 7:13
  • $\begingroup$ @Soke That's not true. I just want to confirm (in an explicit manner) because the answer is for a disbute between me and my teacher. $\endgroup$
    – Bradman175
    May 5, 2016 at 7:30

1 Answer 1

Reset to default
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This is the only interpretation:

After one year, the height is $100\times (5/7)^1$.

After two years, the height is $100\times (5/7)^2$.

...

After ten years, the height is $100\times (5/7)^{10}$.

Now if we use the geometric formula you mentioned, after ten years, the term we look at is actually the eleventh term, and so the formula also gives $100\times (5/7)^{11-1}$.

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    $\begingroup$ Good, Will Hunting! :) $\endgroup$
    – Hypergeometricx
    May 5, 2016 at 6:04
  • $\begingroup$ Unfortunately, that's only half of my question. Prove to me whether the other option is acceptable or not. $\endgroup$
    – Bradman175
    May 5, 2016 at 6:11
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    $\begingroup$ @Bradman175 The answer provided has already quite clearly and adequately shown that the "other option" as you have presented it, is incorrect. That is what "This is the only interpretation to me" means. $\endgroup$
    – heropup
    May 5, 2016 at 6:26
  • $\begingroup$ Now it is clear. Thanks! $\endgroup$
    – Bradman175
    May 5, 2016 at 7:32

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