Question

A small object with an initial temperature of 135 degrees Fahrenheit is dropped into a tub with a temperature of 60 degrees Fahrenheit. The function f(t)=Ce(−kt)+60 represents the situation, where t is time in minutes, C is a constant, and k is a constant. After 6 minutes the object has a temperature of 85 degrees. What is the approximate value of k?

Answer 1

Answer:

0.1831 s⁻¹

Explanation:

The function represents the temperature of the object at a certain time. Because there's a difference in temperature between the object and the tube, heat must flow from the object, and they will achieve thermal equilibrium.

At the beginning, t = 0, the temperature is 135°F, thus:

$135= C*e^{-k*0} + 60$

135 = C + 60

C = 75°F

After 6 minutes, t = 6, the temperature is 85°F, thus:

$85= 75*e^{-k*6} + 60$

$75*e^{-6k} = 25$

$e^{-6k} = 0.3333$

$ln(e^{-6k}) = ln(0.3333)$

-6k = -1.0986

k = 0.1831 s⁻¹