A linear function adds the same amount over equal time steps; an exponential function multiplies by the same factor. A steady rate per hour is your cue to write a starting value plus a rate times time. Then use the rate’s sign to decide whether the function increases or decreases. A negative starting temperature does not mean the temperature is falling.
Hints
- Hint 1
The starting value is the temperature when no time has passed, even if it is below zero. Pair it with the amount added each hour to write a temperature model.
- Hint 2
A linear function adds the same amount each hour, while an exponential function multiplies by the same factor. Does the hourly change describe adding or multiplying?
- Hint 3
To decide increasing or decreasing, look at the change per hour, not the starting temperature. A temperature can start below zero and still rise.
Step-by-step
Build a model from the steady rate
Step 1Write the temperature model
No Desmos needed. The starting temperature and steady hourly rate let you write the model directly.
Let be hours since the outage and be the temperature in degrees Celsius. The freezer starts at and adds each hour, so:
- Step 2
Identify the type of change
A linear function changes by the same added amount for every equal step in time. In , each hour adds , so the steady added amount makes the model linear. An exponential function would multiply by the same factor each hour.
- Step 3
Use the rate to find the direction
The positive hourly rate of means the temperature rises as time passes. The is where it starts, not the direction it moves. The freezer’s temperature is modeled by an increasing linear function. Choice D.