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Nonlinear Functions

SAT Math· difficulty 5/5

A scientist has data showing populations of 400400 at t=0t=0, 500500 at t=2t=2, 625625 at t=4t=4. Which model best fits?

  • A

    y=400t2+400y = 400t^2 + 400

  • B

    y=400+50ty = 400 + 50t

  • C

    y=400(1.118)ty = 400(1.118)^t

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  • D

    y=400(1.25)ty = 400(1.25)^t

Explanation

Ratio: 500/400=1.25500/400 = 1.25 over 2 yrs, so per year 1.25≈1.118\sqrt{1.25} \approx 1.118. Verify: 400(1.118)4≈400⋅1.5625=625400(1.118)^4 \approx 400 \cdot 1.5625 = 625.

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