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Math Help - Exponential Graph help? (Word Problem) 2

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    Exponential Graph help? (Word Problem) 2

    A shipping company owns a fleet of heavy trucks if the purchase price of each truck is $245,000 nad its value depreciates by 15% per year, what ist he value of each truck after 4 years?
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    Quote Originally Posted by puzzledwithpolynomials View Post
    A shipping company owns a fleet of heavy trucks if the purchase price of each truck is $245,000 nad its value depreciates by 15% per year, what ist he value of each truck after 4 years?
    If you imagine that it loses 15% each year then after no time it is at full value, then after one year it is t(1-0.15) and after two t(1-.15)(1-.15) and so after n years we get:

    T(x) = T(0)(1+x)^n

    T(x) is the value at any given value of n
    T(0) is the value at x=0 (ie original value)
    x is the factor of depreciation (x>0 for inflation)
    n = number, in this case years.

    plug in your numbers,
    T(0) = 245,000
    x = -0.15
    n = 4

    T(t) = 245000\cdot(1-0.15)^4 = 127891.53


    --------

    I'll try and explain a bit here:

    T(x) = T(0)(1+x)^n

    the (1+x)^n is because it is gaining/losing a constant amount each year over n years. If was different amounts each time you'd get (1+a)(1+b)(1+c)... and there would be n sets of brackets. However, because it's the same we get (1+x)(1+x)(1+x) n times which is (1+x)^n.
    At n=0 for example we get T(x) = T(0)(1+x)^0 and since a^0 = 1 we get T(x)=T(0) which is what we'd expect from the definitions. As n increase the importance of the (1+x)^n term will increase and it will rapidly exceed T(0), while it will never reach 0 it will become worthless as it'd drop below a cent.
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    Quote Originally Posted by puzzledwithpolynomials View Post
    A shipping company owns a fleet of heavy trucks if the purchase price of each truck is $245,000 nad its value depreciates by 15% per year, what ist he value of each truck after 4 years?
    Hi puzzle,

    We can use the depreciation formula V=a(1-r)^x, where V will represent the present day value after 4 years (x) at a depreciation rate of 15% (r).

    V=245000(1-.15)^4

    V=127891.53

    Or, you could just depreciate 15% a year for 4 years and see what the resulting value would be.

    [End of Year 1] 245000 - .15(245000) = 208250

    [End of Year 2] 208250 - .15(208250) = 177012.50

    [End of Year 3] 177012,50 - .15(177012.50)=150460.625

    [End of Year 4] 150460.625-.15(150460.625)=127891.5313
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