Question

the percentage of area damaged in a fire after t hours of burning is modeled by $p(t) = 12e^{0.08t}$. to the nearest whole number, what percentage of area will be damaged by a fire that burns for eight hours? (1 point)
○ 21 percent
○ 13 percent
○ this is impossible to determine with the information provided
○ 23 percent

Explanation:

Step1: Substitute t = 8 into the function

We have the function \( P(t)=12e^{0.08t} \). When \( t = 8 \), we substitute \( t \) into the function: \( P(8)=12e^{0.08\times8} \)

Step2: Calculate the exponent

First, calculate the exponent: \( 0.08\times8 = 0.64 \)

Step3: Calculate the exponential term

Now, calculate \( e^{0.64} \). Using a calculator, \( e^{0.64}\approx1.8965 \)

Step4: Calculate the final value

Multiply by 12: \( P(8)=12\times1.8965\approx22.758 \), which rounds to 23.

Answer:

23 percent