# Further Maths (just started)

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#1
At the start of the year, a train is half full. Each week the number of people catching this train increases by 1%.
How many weeks will it be before the train is full?

Any help on how to work this out would be appreciated
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5 months ago
#2
I think you use logarithms
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#3
I don't know what those are (I haven't learnt them yet), thanks tho

(Original post by medicalsupernova)
I think you use logarithms
0
5 months ago
#4
(Original post by halpplez)
I don't know what those are (I haven't learnt them yet), thanks tho
I think I can explain it quickly (I just learnt them recently too)
Last edited by medicalsupernova; 5 months ago
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#5
That would be helpful, thank you

(Original post by medicalsupernova)
I think I can explain it quickly (I just learnt them recently too)
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5 months ago
#6
(Original post by halpplez)
At the start of the year, a train is half full. Each week the number of people catching this train increases by 1%.
How many weeks will it be before the train is full?

Any help on how to work this out would be appreciated
Think about what you want to multiply the number by to increase it by 1%, and think about how you're doing this every week (so how will the third week be related to the second?). Hope this helps.
1
5 months ago
#7
(Original post by medicalsupernova)
I think you use logarithms
That is the quickest and easiest method yes.
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5 months ago
#8
https://www.mathsisfun.com/algebra/logarithms.html

Last edited by medicalsupernova; 5 months ago
1
5 months ago
#9
(Original post by medicalsupernova)
https://www.mathsisfun.com/algebra/logarithms.html

Sorry is this GCSE or A-level?

An example and working out:

You can check the formula and number of weeks with any number and it would still work I just used 50 as an example.
Hope this helps
PLEASE edit - it's against the rules to post a solution.
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#10
(Original post by medicalsupernova)
I think I can explain it quickly (I just learnt them recently too)
(Original post by Zoqua)
Think about what you want to multiply the number by to increase it by 1%, and think about how you're doing this every week (so how will the third week be related to the second?). Hope this helps.
Thanks guys, you really helped (I'm doing GCSE further maths)- I'm gonna ask my teacher about logarithms and when we'll go over them. Thanks again
Thanks you for the link as well, it explains them really well
Last edited by halpplez; 5 months ago
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5 months ago
#11
(Original post by Muttley79)
PLEASE edit - it's against the rules to post a solution.
Oh sorry, I didn't know
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5 months ago
#12
I remember this question from GCSE further maths many years ago. It’s unfair because you don’t even learn anything about logarithms at this level. I think they just want you to use trial and error on a calculator.
But it’s compound interest.
After n weeks there will be people on the train. The question asks you when there will be 100 people on the train. So you need to solve an equation from this which uses logarithms - but you don’t strictly need to know about logarithms to solve this, since the logarithm is just a shorthand for writing the solution to a exponential equation basically.

Spoiler:
Show
for example if you could say but to work out it’s decimal expansion. You’re just solving the equation to the level of accuracy that you actually want the solution to be.
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