Question

Initial height of a plant is $50\text{cm}.$ Each day 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 a linear function.
• B. Yes. The function is $h=\frac{1}{2}d,$ where, $h$ is the height in $cm,$ and $d$ is the number of days.
• C. 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 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 $=h\text{cm}$
On the $0^{th}$ day, height $=50\text{cm}$

Each day its height increases by $0.5\text{cm}.$
$\therefore$ In $d$ days, the height will increase by $(0.5\times d)\text{cm}.$
Hence, total height after $d$ days $=(50+0.5\times d)\text{cm}$
$\Rightarrow h=50+0.5\times d$
$\Rightarrow h=50+\frac{1}{2}d$
$\Rightarrow f\left(d\right)=50+\frac{1}{2}d$

This is the required function.
As the exponents of the variables are $1,$ this is a linear function.
Also, the dependent variable $y$ cannot have more than one value for a particular d.