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Nonlinear Functions

SAT Math· difficulty 4/5

An algae mass grows: 5kg5\text{kg} at t=0t=0, 20kg20\text{kg} at t=2t=2 years. Exponential model y=abty=ab^t gives:

  • A

    y=5⋅2ty = 5 \cdot 2^t

  • B

    y=5⋅4ty = 5 \cdot 4^t

  • C

    y=5+7.5ty = 5 + 7.5 t

  • D

    y=5⋅4t/2y = 5 \cdot 4^{t/2}

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Explanation

5b2=20⇒b2=45b^2 = 20 \Rightarrow b^2 = 4, so y=5⋅4t/2y = 5 \cdot 4^{t/2} (equivalent to 5⋅2t5 \cdot 2^t but in form using period 2). Either A or C; C reflects the data period explicitly.

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