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.

23 percent
23 percent

13 percent
13 percent

21 percent

Answer 1

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

First, calculate \( P(8) \):

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

Using a calculator, we find:

\[ e^{0.64} \approx 1.875 \]

Now substitute back into the formula:

\[ P(8) = 12 \times 1.875 \approx 22.5 \]

Rounding to the nearest whole number:

\[ P(8) \approx 23 \]

Therefore, the percentage of the area that will be damaged by a fire that burns for eight hours is 23 percent.