Exponential Growth and Decay Models

AP Calculus AB· difficulty 3/5

Carbon-14 has half-life ~57305730 years. The decay constant kk in y=y0ekty = y_0 e^{kt} is

  • A

    5730/ln25730/\ln 2

  • B

    ln2-\ln 2

  • C

    ln25730-\dfrac{\ln 2}{5730}

    check_circle
  • D

    ln25730\dfrac{\ln 2}{5730}

Explanation

Half-life: e5730k=1/2k=ln2/5730e^{5730 k} = 1/2 \Rightarrow k = -\ln 2/5730.

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