Question

The height of a plant is 50 centimeters. Each day, its height increases by 0.5 centimeters. Can the total height of the plant be represented as a linear function of the number of days? If yes, find the function.

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

Answer 1

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

Let the number of days be $d.$
Let the height of the plant be $h$ cm.
On the $0^{\text{th}}$ day, height = $50$ cm

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

Thus, $h=50+\frac{1}{2}d$ will be 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 $d$.