To find the percentage of area damaged after 8 hours of burning, we can substitute \( t = 8 \) into the given function \( P(t) = 12e^{0.08t} \).
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Calculate \( P(8) \): \[ P(8) = 12e^{0.08 \times 8} \] \[ P(8) = 12e^{0.64} \]
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Calculate \( e^{0.64} \) (using a calculator): \[ e^{0.64} \approx 1.857 \]
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Now, substitute this back into the equation: \[ P(8) \approx 12 \times 1.857 \approx 22.284 \]
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Finally, round to the nearest whole number: \[ P(8) \approx 22 \]
Thus, the percentage of area that will be damaged by the fire after eight hours is approximately 22%.
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