Question

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. \boxed{} °c submit

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay (as a decimal), and $t$ is the time.
Here, $P = 74$, $r = 0.05$ (since 5% = 0.05), and $t = 14$.

Step2: Substitute the values into the formula

Substitute $P = 74$, $r = 0.05$, and $t = 14$ into the formula $A = P(1 - r)^t$.
We get $A = 74(1 - 0.05)^{14}$.

Step3: Calculate $(1 - 0.05)^{14}$

First, calculate $1 - 0.05 = 0.95$.
Then, calculate $0.95^{14}$. Using a calculator, $0.95^{14}\approx0.4877$.

Step4: Calculate the final amount $A$

Multiply $74$ by $0.4877$: $A = 74\times0.4877\approx36.1$.

Answer:

36.1