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Nonlinear Functions

SAT Math· difficulty 5/5

A drug clears with C(t)=C0e−0.2tC(t) = C_0 e^{-0.2 t} where tt is hours. Approximate half-life:

  • A

    22 hours

  • B

    3.53.5 hours

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  • C

    55 hours

  • D

    77 hours

Explanation

e−0.2t=0.5⇒t=ln⁡2/0.2≈0.693/0.2≈3.47e^{-0.2t} = 0.5 \Rightarrow t = \ln 2 / 0.2 \approx 0.693/0.2 \approx 3.47 hours.

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