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anonymous

  • 5 years ago

Can someone solve this please? the points (2,6) and (3,18) lie on the curve y=ax^n use logarithms to find the values of a and n, giving your answers correct to 2d.p. thanks :)

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  1. anonymous
    • 5 years ago
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    Substitute the two points in the given equation, gives us the two following equations: \[6=a(2)^n \rightarrow(1)\] and\[18=a(3)^n \rightarrow(2)\] Now, we should solve the two equations for the two unknowns a and n

  2. anonymous
    • 5 years ago
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    Using the first equation we have: \[a={6 \over 2^n}\rightarrow(*)\] Substitute (*) into equation (2): \[18={6 \over 2^n}(3)^n \implies 3=({3 \over 2})^n \implies \log(3)=n(\log({3 \over 2}))\implies n={\log(3) \over \log({3 \over 2})}\]

  3. anonymous
    • 5 years ago
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    That's n=2.71. Now substitute this value of n into (*) to get a.

  4. anonymous
    • 5 years ago
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    So \[a={6 \over 2^n}={6 \over 2^2.71}\approx0.92\]

  5. anonymous
    • 5 years ago
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    where did the 1 and 2 come from?

  6. anonymous
    • 5 years ago
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    how did you get to \[3=(3/2)^n\]

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