Nonlinear Functions

SAT Math· difficulty 5/5

\Pinvestedat8invested at 8% annual interest compounded continuously equals$P$ doubled in approximately how many years?

  • A

    0.08ln2\dfrac{0.08}{\ln 2}

  • B

    10.08\dfrac{1}{0.08}

  • C

    ln20.08\dfrac{\ln 2}{0.08}

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  • D

    728\dfrac{72}{8} exactly

Explanation

Pe0.08t=2Pt=ln2/0.088.66Pe^{0.08t} = 2P \Rightarrow t = \ln 2 / 0.08 \approx 8.66 years.

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