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Math Help - help finishing of a question

  1. #1
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    Question help finishing of a question

    i have started this , but unable to find a way to complete it, any hints?

    Q: in order to test a model of the form y=ab^x, a student plots a graph of log y against x for her values of x and y. The points lie in a straight line, with the gradient 0.65. the straight line meets the log y axis at the point (0,1.05)
    a) find the values of a and b correct to 1.d.p
    b) hence find the value of y, given by the model, wehn x=3

    Workings so far
    y=ab^x
    logy=logab^x
    logy=loga + xlogb
    logy=xlogb +loga => which in relation is y=mx+c
    i know that loga=1.05 which is where it crosses the y axis
    and that xlogb=0.65 which is the gradient
    but here is where i get stuck. i'm not sure how to reverse log or something like that to work out a and b
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  2. #2
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    Quote Originally Posted by JorCherryhead View Post
    i know that loga=1.05 which is where it crosses the y axis
    and that xlogb=0.65 which is the gradient
    but here is where i get stuck. i'm not sure how to reverse log or something like that to work out a and b
    You have the right idea, but the gradient is not xlogb, but just logb = 0.65, which you can solve for b. ....etc.
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  3. #3
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    how would you find the value for b by using a scientific calc?
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  4. #4
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    Quote Originally Posted by JorCherryhead View Post
    how would you find the value for b by using a scientific calc?
    I wouldn't, but I'm old, and have slide rules, and even tables as well as a calculator and two computers [Google will do claculations for you. Just type it in the search window.] However, ...assuming that you are using logs base 10, use your knowledge of logarithms:

    If log[10]b = 0.65, then b = 10^0.65

    My calculator [which I'll use for this purpose] has a y^x button for this purpose:

    10
    y^x
    0.65
    =
    and I get 4.4668, which you might round.
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  5. #5
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    thankyou again
    yeah using the rule does make things alot simpler. as i was looking at the logb=0.65 and thinking what can i do with this.
    so with the last part of the question, is it just simply subsituting all that i have worked out to find the value of y?
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