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Exponential Growth and Decay Models

AP Calculus AB· difficulty 4/5

A radioactive substance decays per dNdt=−kN\dfrac{dN}{dt} = -kN with half-life 10 years. After 30 years the fraction remaining is

  • A

    14\frac{1}{4}

  • B

    116\frac{1}{16}

  • C

    18\frac{1}{8}

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  • D

    12\frac{1}{2}

Explanation

Three half-lives → (1/2)3=1/8(1/2)^3 = 1/8 remaining.

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