A shifted exponential model has a changing term and a fixed number added outside it. In a cooling problem, a base between and makes the changing term fade, so the fixed number is the level the temperature approaches. Don’t confuse that level with the starting temperature, which also includes the changing term.
Hints
- Hint 1
In a shifted exponential model, the number added outside the power is a fixed baseline. Subtract that number from . Which part of the coffee’s temperature still changes with time?
- Hint 2
The base is between and , so its powers get closer to as time passes. What happens to the coffee’s temperature when the changing part fades?
Step-by-step
Find the temperature the coffee approaches
Step 1Separate the fixed and changing parts
No Desmos needed. The question asks what an added constant means, not for a computed temperature.
Subtract from the model to isolate the changing part:
So is the coffee’s temperature above .
- Step 2
See what happens as the coffee cools
Because is between and , shrinks toward as increases. So the gap above shrinks, and approaches degrees Fahrenheit.
- Step 3
Interpret the temperature in context
As coffee cools, it approaches the temperature of the air around it. So the fixed level a cooling model approaches is the surrounding temperature: degrees Fahrenheit is the temperature of the room. Choice C.