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 174°c and is decreasing by 5% every minute, how much above room temperature will the pan be in 21 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 174°c and is decreasing by 5% every minute, how much above room temperature will the pan be in 21 minutes? if necessary, round your answer to the nearest tenth. °c

Answer

Explanation:

Step1: Identify the decay - formula

The formula for exponential decay is $A = A_0(1 - r)^t$, where $A_0$ is the initial amount, $r$ is the rate of decay as a decimal, and $t$ is the time. Here, $A_0=174$, $r = 0.05$, and $t = 21$.

Step2: Substitute the values into the formula

$A=174\times(1 - 0.05)^{21}$. First, calculate $(1 - 0.05)=0.95$. Then, find $0.95^{21}$. Using a calculator, $0.95^{21}\approx0.3405$.

Step3: Calculate the final value of $A$

$A = 174\times0.3405$. $A\approx59.2$.

Answer:

$59.2$