Mathematics
Suppose a plant has height 1.75 feet and it grows by 0.5 feet each month.
(i) Find the height after 7 months.
(ii) Make a table of values for t varying from 0 to 10 months and show how the height, h, increases every month.
(iii) Find an expression that relates h and t, and explain why it represents linear growth.
Answer
Initial height of the plant = 1.75 feet
Growth per month = 0.5 feet
(i) Height after 7 months = 1.75 + 0.5 × 7
= 1.75 + 3.5
= 5.25 feet
∴ The height of the plant after 7 months is 5.25 feet.
(ii) The height of the plant at the end of t months is given by h = 1.75 + 0.5t.
| Month, t | Height, h (feet) |
|---|---|
| 0 | 1.75 |
| 1 | 2.25 |
| 2 | 2.75 |
| 3 | 3.25 |
| 4 | 3.75 |
| 5 | 4.25 |
| 6 | 4.75 |
| 7 | 5.25 |
| 8 | 5.75 |
| 9 | 6.25 |
| 10 | 6.75 |
(iii) The expression relating h and t is:
h = 1.75 + 0.5t
This represents linear growth because as t (months) increases by 1, the height h increases by a constant value of 0.5 feet. The change in h for every unit change in t is the same, which is the characteristic feature of linear growth.
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