(i) Height after 7 months:

The initial height of the plant is $1.75$ feet, and it grows by $0.5$ feet each month.

Given: Initial height $= 1.75$ feet, Growth rate $= 0.5$ feet/month, Time $= 7$ months

Formula:

$$\text{Height} = \text{Initial height} + (\text{Growth rate} \times \text{Time})$$

Substitution:

$$\text{Height} = 1.75 + (0.5 \times 7)$$

Calculation:

$$\text{Height} = 1.75 + 3.5 = 5.25 \text{ feet}$$

∴ The height after 7 months is 5.25 feet.

(ii) Table of values:

The height increases by a constant amount of $0.5$ feet every month. The table of values for time $t$ (in months) and height $h$ (in feet) is as follows:

$t$	0	1	2	3	4	5	6	7	8	9	10
$h$	1.75	2.25	2.75	3.25	3.75	4.25	4.75	5.25	5.75	6.25	6.75

As shown in the table, the height increases by 0.5 feet every month. This constant increase over equal intervals is a key characteristic of the data provided.

(iii) Expression and explanation:

The expression that relates height $h$ and time $t$ is:

$$h = 1.75 + 0.5t$$

This represents linear growth because, as the value of $t$ increases by a fixed number (one month), the value of the height $h$ increases by a fixed number ($0.5$ feet). A linear pattern where a quantity increases by a constant amount over equal intervals represents linear growth.

∴ The expression is $h = 1.75 + 0.5t$, representing linear growth.