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Posted by on Tuesday, July 3, 2012 at 4:16am.

The mass of a radioactive sample is represented in the graph below. The initial mass of 32 mg decays to 8 mg after 21 hours.

1)What is the half-life of the radioactive sample, in minutes?

2)Solve each equation.
a. 4 8x-1 = 8

b. 3^(2x-5) = 1/27x

  • math30 - , Tuesday, July 3, 2012 at 5:17am

    8 is 1/4 of 32, so two half-lives = 21 hours.

    half-life is 10.5 hours

    4^(8x-1) = (2^2)^(8x-1) = 2^(16x-2) = 8 = 2^3
    so, 16x-2 = 3
    x = 5/16

    assuming 1/27x = (1/27)*x,
    3^(2x-5) = (3^-3)x
    (2x-5)log3 = -3log3 + logx
    (2x-2)log3 = logx
    nope

    assuming a typo, and the x on the right does not belong,

    3^(2x-5) = 1/27 = 3^-3, so
    2x-5 = -3
    x = 1

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