A linear model fits a starting temperature that changes by the same amount each minute. Write the temperature after minutes, then place that expression between the two limits of the inclusive range. Cooling makes the rate negative; it does not reverse which temperature is the lower bound.
Hints
- Hint 1
At a constant rate, the liquid loses the same number of degrees each minute. After minutes, how many degrees has it lost, and what do you subtract that from?
- Hint 2
A compound inequality joins two comparisons involving the same temperature. Inclusive means the temperature may equal either endpoint. How can you check whether each comparison describes the intended range?
- Hint 3
Replace the temperature in your inequality with the expression you built from the starting temperature and the rate. The question asks for an inequality in , not the times at which the liquid reaches each limit.
Step-by-step
Model the temperature, then bound it
Step 1Write the temperature after minutes
No Desmos needed. You're writing an inequality from the story, not solving one.
Let be the liquid's temperature in °C. It starts at °C and loses °C each minute, so after minutes it has lost °C:
- Step 2
Put the inclusive limits around the temperature
“Between °C and °C, inclusive” means is at least and at most . A compound inequality joins both conditions in one chain. Put the temperature between the lower and upper bounds, in that order. Both endpoints count, so use :
- Step 3
Substitute the temperature model
Replace with :
This gives the elapsed times when the liquid's temperature is in the inclusive range. Choice D.