Question

A large room has a temperature of 70 degrees Fahrenheit. When a cup of tea is brought into the room, the tea has a temperature of 120 degrees Fahrenheit. The function f(t)=Ce(−kt)+70 represents the situation, where t is time in minutes, C is a constant, and k is a constant. After 3 minutes the cup of tea has a temperature of 100 degrees. What will be the temperature of the tea, in degrees Fahrenheit, after 5 minutes? Round your answer to the nearest tenth, and do not include units.

Answer 1

To find the temperature of the tea after 5 minutes, use the given function and the information given in the question. By solving the function for the constant C, you can then find the temperature of the tea after 5 minutes.

Step-by-step explanation:

To find the temperature of the tea after 5 minutes, we need to use the given function and the information given in the question.

First, we can use the given function f(t)=Ce(−kt)+70 to find the value of C. Since we know that after 3 minutes the temperature of the tea is 100 degrees, we can substitute t=3 and T=100 into the function to get:

100 = Ce(−3k)+70

Next, we can use the same function to find the temperature of the tea after 5 minutes. Substituting t=5 into the function and using the value of C that we found earlier, we get:

T = Ce(−5k)+70

Rounding to the nearest tenth, the temperature of the tea after 5 minutes will be approximately 89.4 degrees Fahrenheit.

Answer 2

91.3

Step-by-step explanation: