Question

while sam was at work, his house lost electrical power. by the time the electrical power came back on, the temperature inside the house was 88°f. the air conditioner immediately started to cool the house. let f(x) represent the temperature, in degrees fahrenheit, of sam’s house x minutes after the air conditioner started to cool the house. part a: what is the meaning of the statement f(30) = 76? a. after 30 minutes, the house has cooled to 76°f. b. after 30 minutes, the house is 76°f cooler than it was when the air conditioner started to cool the house. c. after 76 minutes, the house has cooled to 30°f. d. after 76 minutes, the house is 30°f cooler than it was when the air conditioner started to cool the house.

Explanation:

The function \( f(x) \) represents the temperature of Sam's house \( x \) minutes after the air conditioner starts cooling. So \( f(30) = 76 \) means when \( x = 30 \) (30 minutes after the AC starts), the temperature \( f(x) \) is 76°F. Option A correctly interprets this: after 30 minutes, the house has cooled to 76°F. Option B misinterprets the function as a temperature difference, C swaps the input and output, and D also misinterprets the function's meaning.

Answer:

A. After 30 minutes, the house has cooled to 76°F.