Question

A can of soda is placed inside a cooler. As the soda cools, its temperature in degrees Celsius is given by the following function, where is the number of minutes since the can was placed in the cooler. Find the initial temperature of the soda and its temperature after 15 minutes.

Round your answers to the nearest degree as necessary.
T(x) = -7 + 25e⁻⁰.⁰⁴⁵ˣ

Answer 1

The question involves an exponential decay function used to model the cooling of a soda. The initial temperature of the soda is 18°C, and after 15 minutes it cools to approximately 5°C.

Step-by-step explanation:

The subject of this question is Mathematics, and it pertains to the topic of functions, specifically exponential decay in the context of cooling. To find the initial temperature of the soda, we evaluate the function T(x) at x = 0, since x represents the number of minutes since the can was placed in the cooler. The formula given is T(x) = -7 + 25e-0.045x. When x = 0, T(0) = -7 + 25e-0.045(0) = -7 + 25(1) = 18°C.

After 15 minutes, we substitute x = 15 into the function to find T(15) = -7 + 25e-0.045(15). Using a calculator, we find that this expression rounds to approximately 5°C to the nearest degree. Therefore, the initial temperature of the soda was 18°C, and the temperature after 15 minutes is approximately 5°C.