The height of water in a cylindrical tank is 3 m at the start of summer. The height h m at the end of t months is given by the linear function h(t) = 3 − 0.5t.
What will be the height of the water at the end of 5 months?
Answer: h(5) = 3 − 0.5 × 5 = 0.5 m.
Step-by-step solution
Given: h(t) = 3 − 0.5t
Idea: Substitute t = 5 in the function.
- h(5) = 3 − 0.5 × 5 = 3 − 2.5½ mark
- = 0.5 m. (This continues the table: 1 m at 4 months, then 0.5 m less.)½ mark
The height of the water at the end of 5 months will be 0.5 m.
Check: From the table, h(4) = 1 m; one more month takes away 0.5 m, giving 0.5 m ✓.
Answer to write in the exam
h(5) = 3 − 0.5(5) = 3 − 2.5
∴ Height at the end of 5 months = 0.5 m
Common mistakes that cost marks
- Working out 3 − 0.5 × 5 as (3 − 0.5) × 5 = 12.5. Multiply before subtracting.
- Writing 0.5 × 5 = 0.25.
- Giving the answer without units.
How this can come in the exam
MCQ (1 mark)
For h(t) = 3 − 0.5t, the tank becomes empty after
- 5 months
- 6 months
- 3 months
- 1.5 months
Show answer
(B) 6 months
3 − 0.5t = 0 ⇒ t = 6.
Short answer (2 marks)
A pond is 2.4 m deep and its depth falls by 0.3 m every week. Write the depth after w weeks and find it after 5 weeks.
Show answer
D(w) = 2.4 − 0.3w (1 mark). D(5) = 2.4 − 1.5 = 0.9 m (1 mark).Try one yourself
Using h(t) = 3 − 0.5t, find the height after 2.5 months.
Show answer
3 − 1.25 = 1.75 m.
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