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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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