Question

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%**