Question

the function $f(t)$ models the temperature, in degrees celsius, $t$ hours after midnight. use function notation to represent each statement. the temperature at 2 am. the temperature was the same at 9 am and at 11 am. the temperature was higher at 9 am than at 2 am. $t$ hours after midnight, the temperature was $24\degree$c.

Explanation:

Step1: Temperature at 2 AM

2 AM is 2 hours after midnight, so substitute \( t = 2 \) into \( f(t) \).
\( f(2) \)

Step2: Same temperature at 9 AM and 11 AM

9 AM is 9 hours after midnight (\( t = 9 \)), 11 AM is 11 hours after midnight (\( t = 11 \)). Set their function values equal.
\( f(9) = f(11) \)

Step3: Higher at 9 AM than 2 AM

9 AM: \( t = 9 \) ( \( f(9) \) ), 2 AM: \( t = 2 \) ( \( f(2) \) ). Use inequality for "higher".
\( f(9) > f(2) \)

Step4: Temperature 24°C at \( t \) hours

Substitute \( f(t) = 24 \) as the temperature is 24°C at \( t \) hours.
\( f(t) = 24 \)

Answer:

• The temperature at 2 AM: \( \boldsymbol{f(2)} \)
• The temperature was the same at 9 AM and at 11 AM: \( \boldsymbol{f(9) = f(11)} \)
• The temperature was higher at 9 AM than at 2 AM: \( \boldsymbol{f(9) > f(2)} \)
• \( t \) hours after midnight, the temperature was 24°C: \( \boldsymbol{f(t) = 24} \)