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)

Question

Responses

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

23 percent
23 percent

21 percent
21 percent

13 percent

Answer 1

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

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

\[ P(8) = 12e^{0.08 \cdot 8} \] \[ = 12e^{0.64} \] Using the approximate value of \( e^{0.64} \) (which is about 1.8573):

\[ = 12 \cdot 1.8573 \approx 22.2876 \]

Now rounding to the nearest whole number, we get:

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

Based on the responses you provided, the closest option to this value is 23 percent.