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Math Help - 2^(3.2)

  1. #1
    Junior Member
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    Question 2^(3.2)

    Estimate 2^(3.2) to tenths without using a calculator and I need to show my arithmetic.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Mar 2009
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    Florida
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    Sadieann

    If you use the tangent line approximation

    f(x+dx) = f(x)+f ' (x) dx

    f(3+.2) = 2^3 + ln(2)*2^3*.2 = 9.11 exact 2^3.2 = 9.19

    I don't see how to do this completely without a calulator unless you know ln(2) is .693 and you multiply by hand but that seems silly
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