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    Hi, I'm trying to practise C2 logs as they are my weak point but its quite frustrating as I have a question that doesn't stick to the rules:

    A car was purchased for £18 000 on 1st January.
    On 1st January each following year, the value of the car is 80% of its value on 1st January in the
    previous year.

    The value of the car falls below £1000 for the first time n years after it was purchased.
    (b) Find the value of n.

    To solve, they put ar^n but surely its meant to be ar^n-1???

    I also find it confusing because whenever I'm working out a question like this, I always get the no. of years at the end wrong. Sometimes they use n and sometimes n-1

    Thank you for your help!
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    (Original post by djels013.211)
    Hi, I'm trying to practise C2 logs as they are my weak point but its quite frustrating as I have a question that doesn't stick to the rules:

    A car was purchased for £18 000 on 1st January.
    On 1st January each following year, the value of the car is 80% of its value on 1st January in the
    previous year.

    The value of the car falls below £1000 for the first time n years after it was purchased.
    (b) Find the value of n.

    To solve, they put ar^n but surely its meant to be ar^n-1???

    I also find it confusing because whenever I'm working out a question like this, I always get the no. of years at the end wrong. Sometimes they use n and sometimes n-1

    Thank you for your help!
    It's usually possible to clarify this kind of situation by writing out the first few terms of the sequence, taking careful note of how the question is worded. In this case,

    After 0 years, value = a
    After 1 year, value = ar
    After 2 years, value = ar^2
    therefore
    After n years, value = ar^n

    A similar problem can come up in other questions that refer to calendar years, e.g.

    n = 1, Y = 2013
    n = 2, Y = 2014
    n = 3, Y = 2015 etc

    In such cases, I find that establishing a mathematical relationship between n and Y, after writing out the first few terms of the sequence, can help to avoid year confusion. In this case,

    Y = n + 2012 and n = Y - 2012

    Then, if you derive an answer of say n = 11, you can quickly determine that the corresponding year Y = 11 + 2012 = 2023.
 
 
 
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