Question

A cup of coffee at 90 degrees celsius is put into a 20 degree celsius room at t = 0 . The coffee's temperature is changing at a rate of r ( t ) = − 7 e − 0.1 t degrees celsius per minute, with t in minutes. Estimate the coffee's temperature when t = 10 .

Answer 1

Answer: 58.72 degrees Celsius.

Explanation:

We can use the following formula to estimate the temperature of the coffee when t = 10:

T(t) = T(room) + [T(initial) - T(room)] * e^(-r(t) * t)

where T(t) is the temperature of the coffee at time t, T(room) is the temperature of the room, T(initial) is the initial temperature of the coffee, and r(t) is the rate of change of the coffee's temperature.

Substituting the given values, we get:

T(10) = 20 + [90 - 20] * e^(-(-7 e^(-0.1 * 10)) * 10)

T(10) = 20 + 70 * e^(0.7)

T(10) ≈ 58.72 degrees Celsius (rounded to two decimal places)

Therefore, the estimated temperature of the coffee when t = 10 is 58.72 degrees Celsius.