Question

A bowl of cold gazpacho soup is warming to room temperature.the temperature difference between the soup and the room decreases by 5% every minute. What will the temperature difference be in 5 minutes if it is currently 16°C

Answer 1

The temperature difference in 5 minutes will be 12.38ºC

Explanation:

The difference in temperature after t minutes is given by the following equation:

`T(t) = T(0)(1-r)^(t)`

In which T(0) is the initial temperature and r is the decrease rate, as a decimal.

Decreases by 5% every minute.

This means that
`r = 0.05`

What will the temperature difference be in 5 minutes if it is currently 16°C

This is T(5) when
`T(0) = 16`

So

`T(t) = T(0)(1-r)^(t)`

`T(t) = 16(1-0.05)^(t)`

`T(t) = 16*(0.95)^(t)`

`T(5) = 16*(0.95)^(5) = 12.38`

The temperature difference in 5 minutes will be 12.38ºC