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Further Maths (just started)

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 :smile:
I think you use logarithms
Reply 2
I don't know what those are (I haven't learnt them yet), thanks tho :smile:

Original post by medicalsupernova
I think you use logarithms
Original post by halpplez
I don't know what those are (I haven't learnt them yet), thanks tho :smile:

I think I can explain it quickly (I just learnt them recently too)
(edited 3 years ago)
Reply 4
That would be helpful, thank you

Original post by medicalsupernova
I think I can explain it quickly (I just learnt them recently too)
Reply 5
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 :smile:


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.
Reply 6
Original post by medicalsupernova
I think you use logarithms


That is the quickest and easiest method yes.
(edited 3 years ago)
Original post by medicalsupernova
https://www.mathsisfun.com/algebra/logarithms.html

I think this link is helpful :smile:

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 :smile:

PLEASE edit - it's against the rules to post a solution.
Reply 9
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 :smile: (I'm doing GCSE further maths)- I'm gonna ask my teacher about logarithms and when we'll go over them. Thanks again :smile:
Thanks you for the link as well, it explains them really well
(edited 3 years ago)
Original post by Muttley79
PLEASE edit - it's against the rules to post a solution.

Oh sorry, I didn't know :smile:
Reply 11
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 50×1.01n 50\times 1.01^n 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.

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