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vlabodo [156]
3 years ago
12

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 incr

eased to 10°C. (Round your answers to two decimal places.) (a) What is the temperature of the drink after 55 minutes?

Mathematics
1 answer:
Andrews [41]3 years ago
3 0

Answer:

  (a)  13.85 °C

Step-by-step 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.

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