Question

A cup of hot water is left out to cool. The water is currently 19°C above room temperature. If the heat difference decreases by 5% every minute, what will the difference be in 13 minutes?

Answer 1

`\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &19\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ t=minutes\dotfill &13\\ \end{cases} \\\\\\ A = 19(1 - 0.05)^(13) \implies A = 19( 0.95 )^(13)\implies A \approx 9.75`