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C2 Geometric sequence question

satisverborum2003

The fish in a particular area of the north sea are being reduced by 6% each year due to overfishing. How long would it be before the fish stocks are halved?

I would be grateful if someone can show me the working out to get to the answer.

Reply 1

Dr. Unk

It's quite simple, actually. You have to find 0.94^n = 0.5 and then turn n into years and months. :smile:

Reply 2

BJack

The amount of fish left after

n

years is

ar^n

where a is the starting amount of fish and r is the common ratio.

Reply 3

frisco97

Original post by satisverborum2003

First take 6% from 100% which would be the common ratio r. The answer would be r=0.94.
You would have to take logs to work out the answer to this question.
log(0.94)^x>log(0.5
x>log(0.5 / log(0.95
x= 11.2 years (3 sig.fig )