Question

let ( f(t) ) be the temperature of a cup of coffee ( t ) minutes after it has been poured. interpret ( f(6) = 130 ) and ( f(6) = -7 ). estimate the temperature of the coffee after 6 minutes and 12 seconds, that is, after 6.2 minutes. what does ( f(6) = 130 ) imply?
a. 130 minutes after the coffee has been poured, the temperature of the cup of coffee is rising at a rate of 6 degrees per minute.
b. 6 minutes after the coffee has been poured, the temperature of the cup of coffee is rising at a rate of 130 degrees per minute.
c. 6 minutes after the coffee has been poured, the temperature of the cup of coffee is 130 degrees.
d. 130 minutes after the coffee has been poured, the temperature of the cup of coffee is 6 degrees.

Explanation:

The function \( f(t) \) represents the temperature of the coffee \( t \) minutes after it is poured. So \( f(6) = 130 \) means that when \( t = 6 \) (6 minutes after pouring), the temperature \( f(t) \) is 130 degrees. Option A and B refer to rates (related to the derivative \( f'(t) \), not \( f(t) \) itself), and option D misinterprets the input and output of the function. Option C correctly states that 6 minutes after pouring, the coffee's temperature is 130 degrees.

Answer:

C. 6 minutes after the coffee has been poured, the temperature of the cup of coffee is 130 degrees.