Question

A cup of hot water is left out to cool. The water is currently 88°C above room temperature. If the heat difference decreases by 6% every minute, what will the difference be in 6 minutes? Round your answer to the nearest tenth of a degree.

Answer 1

Step 1: Write out the formula.

Let T be the heat difference per minute between the hot water and the room temperature.

Therefore,

`\begin{gathered} T_{}(t)=88(0.94)^t \\ \end{gathered}`
`\begin{gathered} \text{ Where} \\ t\text{ is the time in minutes} \end{gathered}`

Step 2: Compute the difference in 6 minutes

In 6 minutes,

`t=6`

Therefore,

`T(6)=88(0.94)^6=60.7^0C`

Therefore the difference in 6 minutes is 60.7°C