Question

When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C room its temperature has increased to 10°C. (Round your answers to two decimal places.) (a) What is the temperature of the drink after 55 minutes?

Answer 1

(a) 13.85 °C

Explanation:

The temperature difference is a decaying exponential function of time. Here, it decreases from an initial difference of 15 °C to 10 °C after 25 minutes. So, that temperature difference can be modeled as ...

ΔT = 15(10/15)^(t/25)

We want to find the value of this at t=55. It is ...

ΔT = 15(2/3)^(55/25) ≈ 6.15

This is the amount the temperature of the drink is below room temperature.

drink temperature = (20 - 6.15) °C = 13.85 °C

The temperature of the drink after 55 minutes is about 13.85 °C.