Answer :
Final answer:
Option b is the correct answer. The expression h(40) = 81 indicates that after 40 minutes, the house temperature is 81°F. A 40.0°F decrease is equivalent to a 22.22°C decrease, confirming that the change in Fahrenheit degrees is nine-fifths the change in Celsius degrees.
Explanation:
The expression h(40) = 81 in the context of the problem provided likely means that after 40 minutes, the temperature in the house has been cooled to 81°F. This is under the assumption that h represents the temperature function of the house concerning time in minutes, and 81 represents the temperature reading in Fahrenheit after a certain amount of time has elapsed.
To answer the question of how much the temperature decreases in degrees Celsius when there's a 40.0°F decrease, we first convert the Fahrenheit change to Celsius using the formula: C = 5/9(F - 32), where F is the change in Fahrenheit. However, because we are measuring a change in temperature, the formula simplifies to ∆C = 5/9 × ∆F, which means a decrease of 40°F is equivalent to ∆C = 5/9 × 40 = 22.22°C. This shows that any change in temperature in Fahrenheit degrees is indeed nine-fifths the change in Celsius degrees as demanded by part (b).
