The temperature , in degrees Celsius, of a pot of soup as it cools is modeled by the function
where is the time, in hours, since the soup was removed from heat, and is the constant room temperature.
Which statement is the best interpretation of the number in this context?
In a shifted exponential model such as , is a fixed baseline and is the gap above it. To interpret , use the starting time : the power becomes , so is the initial gap, not the total starting value. You can check by evaluating the function in Desmos and subtracting the baseline.
Hints
- Hint 1
The baseline is the fixed number added outside the power. Here, room temperature stays fixed while the soup cools. Which part of the expression measures the soup’s temperature above room temperature?
- Hint 2
The initial temperature is the temperature at , when the soup was removed from heat. Any nonzero number raised to the power is . What does that do to the changing part of the model?
Step-by-step
Find the starting gap above room temperature
Step 1Separate the gap from room temperature
The problem calls the constant room temperature, or baseline. Subtract to show the gap above it: . The room temperature stays fixed; only this gap shrinks.
- Step 2
Find the total starting temperature
At , the soup has been removed from heat, and . Type , then in Desmos. It shows , the total starting temperature in degrees Celsius, not what alone means.
- Step 3
Interpret the starting gap
Type on the next line. Desmos shows . So the coefficient gives the starting gap above the baseline: the soup initially was above room temperature, not in total. Choice C.