The percentage of area damaged in a fire after t hours of burning is modeled by P(t)=12e0.08t

Question

. To the nearest whole number, what percentage of area will be damaged by a fire that burns for eight hours?(1 point)
Responses

This is impossible to determine with the information provided.
This is impossible to determine with the information provided.

21 percent
21 percent

23 percent
23 percent

13 percent

Answer 1

To determine the percentage of area damaged by a fire that burns for eight hours, we can use the given function \( P(t) = 12e^{0.08t} \).

1. Substitute \( t = 8 \) into the formula: \[ P(8) = 12e^{0.08 \times 8} \]

2. Calculate \( 0.08 \times 8 = 0.64 \).

3. Now we have: \[ P(8) = 12e^{0.64} \]

4. Calculate \( e^{0.64} \) (approximately 1.857).

5. Therefore, \[ P(8) = 12 \times 1.857 \approx 22.284 \]

6. Rounding to the nearest whole number gives us \( 22 \) percent.

Based on the provided options, the closest answer would be 23 percent.