Exponential Growth and Decay Models

AP Calculus AB· difficulty 3/5

A bacteria population doubles every 33 hours. Its growth constant kk satisfies e3k=2e^{3k} = 2, so k=k =

  • A

    3ln23 \ln 2

  • B

    ln23\dfrac{\ln 2}{3}

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  • C

    13ln2\dfrac{1}{3 \ln 2}

  • D

    ln2\ln 2

Explanation

3k=ln2k=(ln2)/33k = \ln 2 \Rightarrow k = (\ln 2)/3.

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