The percentage of area damaged in a fire after t hours of burning is modeled by P(t)=12e0.08t . To the nearest whole number, what percentage of area will be damaged by a fire that burns for eight hours?(1 point)

Answer 1

To find the percentage of area damaged by the fire after 8 hours, we can substitute \( t = 8 \) into the model \( P(t) = 12e^{0.08t} \).

First, calculate the exponent:

\[ 0.08 \times 8 = 0.64 \]

Now, we can evaluate \( P(8) \):

\[ P(8) = 12e^{0.64} \]

Next, we need to calculate \( e^{0.64} \). Using a calculator, we find:

\[ e^{0.64} \approx 1.857 \]

Now plug this value back into the equation:

\[ P(8) = 12 \times 1.857 \approx 22.284 \]

Finally, we round \( 22.284 \) to the nearest whole number:

\[ \text{Percentage of area damaged} \approx 22% \]

Therefore, the final answer is:

22%