Question

$\text{Initial height of a plant is}50\text{cm. Each day}$
$\text{its height increases by}0.5\text{cm. Can the total}$
height of the plant be represented as a linear function of number of days? If yes, obtain the function.

• A. No. It will not result in a linear function.
• B. $\text{Yes. The function is}h=\frac{1}{2}d,$
  where, h is the height in cm, and d is the number of days.
• C. $\text{Yes. The equation is}h=50+\frac{1}{2}d,$ where, h is the height in cm, and d is the number of days.
• D. It is a relation but not a function.

Answer 1

The correct option is C $\text{Yes. The equation is}h=50+\frac{1}{2}d,$ where, h is the height in cm, and d is the number of days.

Let, number of days = d
Height of the plant = h cm

$\text{On the}{0}^{th}\text{day, height}=50\text{cm}$

$\text{Each day its height increases by}0.5\text{cm.}$

Slope (m) = Unit rate of change = 0.5 cm every day

$\therefore \text{In "d" days, the height increases by}$
$(0.5\times d)\text{cm}.$

Initial height of the plant (b) = 50 cm

Hence, total height after "d" days
$=(50+0.5\times d)\text{cm}$
$\Rightarrow h=50+0.5\times d$
$\Rightarrow h=50+\frac{1}{2}d$

So, the equation y = mx + b can also be $\text{written as}h=50+\frac{1}{2}d$
Where,
y = h = Total height of the plant
x = d = Number of days
b = Initial height of plant

As the exponents of all the variables are 1, this is a linear function.