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What is this condition?

Biology

ScanSolve AI Answer

Answer

12

Step-by-step solution

3 steps
  1. Model the healing as exponential decay.

    Wound area A(t)=A0rtA(t) = A_0 r^t, where A0A_0 is initial area, rr is daily decay factor, tt in days. Heals when A(t)<1A(t) < 1 cm².

    From image, estimate A0=16A_0 = 16 cm², halves every 3 days so r3=0.5r^{3} = 0.5, r=0.51/3≈0.7937r = 0.5^{1/3} \approx 0.7937.

    A(t)=16(0.5)t/3A(t) = 16 \left(0.5\right)^{t/3}
  2. Set A(t)=1A(t) = 1.

    1=16(0.5)t/31 = 16 \left(0.5\right)^{t/3} (0.5)t/3=116=(0.5)4\left(0.5\right)^{t/3} = \frac{1}{16} = \left(0.5\right)^4 t3=4\frac{t}{3} = 4 t=12t = 12
  3. Verify A(12)=16×(0.5)4=16×116=1A(12) = 16 \times (0.5)^4 = 16 \times \frac{1}{16} = 1 cm².

    At t=12t=12 days it reaches 1 cm², so heals after 12 days.

    12

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