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.

Explanation:

Step1: Identify decay formula

This is exponential decay, use $A = P(1-r)^t$, where $P=74$, $r=0.05$, $t=14$.

Step2: Calculate remaining factor

First compute $(1-0.05)^{14} = 0.95^{14}$.
$0.95^{14} \approx 0.48767$

Step3: Compute final temperature difference

Multiply initial difference by the factor: $74 \times 0.48767$
$74 \times 0.48767 \approx 36.1$

Answer:

$36.1$ °C