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Question

Initial height of a plant is 50 cm. Each day its height increases by 0.5 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.
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B
Yes. The function is h=12d, where, h is the height in cm, and d is the number of days.
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C
Yes. The equation is h=50+12d, where, h is the height in cm, and d is the number of days.
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D
It is a relation but not a function.
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Solution

The correct option is C Yes. The equation is h=50+12d, 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
On the 0th day, height =50 cm

Each day its height increases by 0.5 cm.
In d days, the height will increase by (0.5×d) cm.
Hence, total height after d days =(50+0.5×d) cm
h=50+0.5×d
h=50+12d
f(d)=50+12d

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.

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