The percentage of area damaged in a fire after t hours of burning is modeled by P(t)=12e^0.08t

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 8 hours using the given model \( P(t) = 12e^{0.08t} \), we need to substitute \( t = 8 \) into the equation.

Calculating \( P(8) \):

\[ P(8) = 12e^{0.08 \times 8} \] \[ P(8) = 12e^{0.64} \]

Now, we need to calculate \( e^{0.64} \). Using a calculator, \( e^{0.64} \) is approximately 1.857.

Now substitute back into the equation:

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

Rounding this to the nearest whole number gives us:

\[ P(8) \approx 22% \]

So, the closest percentage option to choose is 23 percent.