The problem states that function $f$ gives the temperature in degrees Celsius, $t$ hours after midnight. We need to choose the equation that represents the statement "At 1:30 p.m., the temperature was 20 degrees Celsius."

1. Problem Description

The problem states that function $f$ gives the temperature in degrees Celsius, $t$ hours after midnight. We need to choose the equation that represents the statement "At 1:30 p.m., the temperature was 20 degrees Celsius."

2. Solution Steps

First, we need to convert 1:30 p.m. to hours after midnight. Since 1:00 p.m. is 13:00 in 24-hour time, 1:30 p.m. is 13:

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0. To convert this to hours, we have 13 hours and 30 minutes.

We can convert 30 minutes to hours by dividing by 60:

$\frac{30}{60} = 0.5$ hours.

So, 13:30 is equal to 13.5 hours after midnight.

Since the temperature at 1:30 p.m. (which is 13.5 hours after midnight) was 20 degrees Celsius, we have $f(13.5) = 20$.

3. Final Answer

D. $f(13.5) = 20$