a pot of soup, currently 74°c above room temperature, is left out to cool. if that temperature difference…

a pot of soup, currently 74°c above room temperature, is left out to cool. if that temperature difference decreases by 5% per minute, then what will the difference be in 14 minutes? if necessary, round your answer to the nearest tenth. °c

a pot of soup, currently 74°c above room temperature, is left out to cool. if that temperature difference decreases by 5% per minute, then what will the difference be in 14 minutes? if necessary, round your answer to the nearest tenth. °c

Answer

Explanation:

Step1: Identify the formula for exponential decay

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, $P = 74$, $r=0.05$, and $t = 14$.

Step2: Substitute the values into the formula

$A=74\times(1 - 0.05)^{14}=74\times0.95^{14}$.

Step3: Calculate $0.95^{14}$

Using a calculator, $0.95^{14}\approx0.4877$.

Step4: Calculate the final value of $A$

$A = 74\times0.4877\approx36.1$.

Answer:

$36.1$