AlgebraMediumInterpreting the intercept in a decreasing model
Algebra practice question
The function w(t) = 18 − 1.5t models the depth, in centimetres, of water in a paddling pool t hours after a leak begins. Which statement is the best interpretation of the number 18?
- A. The pool was 18 centimetres deep when the leak began.Correct
- B. The pool empties after 18 hours.
- C. The pool loses 18 centimetres per hour.
- D. The pool was 18 centimetres deep after 1 hour.
Answer: A. The pool was 18 centimetres deep when the leak began.
w(0) = 18: the depth at the start of the leak.
Why the other answers are wrong
- B. The pool empties after 18 hours.
- It empties when 18 − 1.5t = 0, at 12 hours.
- C. The pool loses 18 centimetres per hour.
- The rate of loss is 1.5 cm per hour.
- D. The pool was 18 centimetres deep after 1 hour.
- After 1 hour the depth is 16.5.
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