Question 7·Easy·Two-Variable Data: Models and Scatterplots
After a power outage, the temperature inside a freezer rises from −18 °C at a steady rate of 2 °C per hour. What type of function best models the relationship between the freezer’s internal temperature and elapsed time?
For questions asking what type of function fits a situation, first decide whether the change is by a constant amount (linear) or by a constant factor (exponential). Then determine whether the quantity goes up (increasing) or down (decreasing) as time increases. Match these two decisions (linear vs. exponential, increasing vs. decreasing) directly to the wording of the answer choices.
Hints
Use the phrase "steady rate"
Focus on the words "rises from −18 °C at a steady rate of 2 °C per hour." What does it mean about how much the temperature changes each hour?
Linear vs. exponential
Ask yourself: is the temperature being changed by adding the same amount each hour, or by multiplying by the same factor each hour?
Direction of change
As time passes after the power outage, does the temperature inside the freezer go up or go down? Use that to decide between "increasing" and "decreasing" in the answer choices.
Desmos Guide
Graph the temperature function
In Desmos, type T(x) = -18 + 2x to represent the temperature after hours. Look at the graph’s shape and note whether it is a straight line and whether it goes up or down as increases.
Compare with exponential shapes (optional check)
Type an example of exponential growth like y = 2^x and an example of exponential decay like y = (1/2)^x. Compare these curved graphs to your temperature graph to see whether the freezer situation looks more like a straight line or a curve, and whether it is going up or down over time.
Step-by-step Explanation
Translate the situation into a rate of change
The problem says the temperature rises from −18 °C at a steady rate of 2 °C per hour.
- "Steady rate" means the same amount is added each hour.
- Every 1 hour, the temperature increases by exactly degrees.
This tells you the change in temperature per hour is constant.
Connect constant rate with function type
A linear function changes by the same amount each unit of time (constant rate of change or constant slope).
An exponential function changes by multiplying by the same factor each step, so the amount of change itself keeps getting bigger or smaller.
Here, the temperature is going up by 2 °C every hour, not by a growing or shrinking amount. That matches a linear pattern, not an exponential one.
Decide if the function is increasing or decreasing
The temperature starts at °C and rises by °C each hour.
- After 1 hour: °C
- After 2 hours: °C
These numbers are getting larger (moving toward and past ), so the function is increasing as time increases.
A simple model would look like:
This is a straight line that goes up as increases, so the correct description is an increasing linear function (choice D).