a pan from the oven is sitting out to cool to room temperature. if the temperature difference between the…

a pan from the oven is sitting out to cool to room temperature. if the temperature difference between the pan and room temperature is currently 197°c and is decreasing by 6% every minute, how much above room temperature will the pan be in 15 minutes? if necessary, round your answer to the nearest tenth. °c

a pan from the oven is sitting out to cool to room temperature. if the temperature difference between the pan and room temperature is currently 197°c and is decreasing by 6% every minute, how much above room temperature will the pan be in 15 minutes? if necessary, round your answer to the nearest tenth. °c

Answer

Explanation:

Step1: Identify the decay formula

The formula for exponential decay is $A = P(1 - r)^t$, where $P$ is the initial amount, $r$ is the rate of decay as a decimal, and $t$ is the time. Here, $P = 197$, $r=0.06$, and $t = 15$.

Step2: Substitute the values into the formula

$A=197\times(1 - 0.06)^{15}=197\times0.94^{15}$.

Step3: Calculate $0.94^{15}$

Using a calculator, $0.94^{15}\approx0.3957$.

Step4: Calculate the final value of $A$

$A = 197\times0.3957\approx78.0$.

Answer:

$78.0$