AlgebraVery hardInterpreting a small negative slope
Algebra practice question
The function T(d) = 15 − 0.0065d models the air temperature T, in degrees Celsius, at a height of d metres above a town. Which of the following is the best interpretation of the number 0.0065 in this context?
- A. The temperature decreases by 0.0065 degrees Celsius for each additional metre of height.Correct
- B. The temperature at ground level is 0.0065 degrees Celsius.
- C. The temperature is 0 degrees Celsius at a height of 0.0065 metres.
- D. The temperature increases by 0.0065 degrees Celsius for each additional metre of height.
Answer: A. The temperature decreases by 0.0065 degrees Celsius for each additional metre of height.
The coefficient of d is the change in T per metre, and its sign is negative.
Why the other answers are wrong
- B. The temperature at ground level is 0.0065 degrees Celsius.
- The ground-level temperature is the constant, 15.
- C. The temperature is 0 degrees Celsius at a height of 0.0065 metres.
- T = 0 at d = 15/0.0065, about 2,300 metres.
- D. The temperature increases by 0.0065 degrees Celsius for each additional metre of height.
- The slope is negative, so the temperature falls.
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