Question

A cup of hot coffee has been left to cool in a room with an ambient temperature of 21C.

The relationship between the elapsed time, m, in minutes, since the coffee was left to cool, and the temperature of the coffee, T, measured in C ∘, is modeled by the following function.
T(m)=21+74*10^-0.03m
What will the temperature of the coffee be after 10 minutes?

Answer 1

Using the function T(m) = 21 + 74 × 10^-0.03m, the temperature of the coffee after 10 minutes is approximately 58°C.

Step-by-step explanation:

The subject of this question is Mathematics, more specifically, it relates to functions and their application in real-world problems, such as the cooling of a cup of coffee over time. The question falls within the High School grade level.

To calculate the temperature of the coffee after 10 minutes, we can substitute the value of m (elapsed time) into the given function T(m) = 21 + 74 × 10^-0.03m. For m = 10 minutes, the calculation would be:

T(10) = 21 + 74 × 10^-0.03×10

T(10) = 21 + 74 × 10^-0.3

T(10) = 21 + 74 × (0.5) (approximately)

T(10) = 21 + 37

T(10) = 58°C

Therefore, after 10 minutes, the temperature of the coffee will be approximately 58°C.