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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
Yes. The function is h=12d,
where, h is the height in cm, and d is the number of days.
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B
It is a relation but not a function.
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C
No. It will not result in a linear function.
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D
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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Solution

## The correct option is D 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. Slope (m) = Unit rate of change = 0.5 cm every day ∴ In "d" days, the height increases by (0.5×d) cm. Initial height of the plant (b) = 50 cm Hence, total height after "d" days =(50+0.5×d) cm ⇒h=50+0.5×d ⇒h=50+12d So, the equation y = mx + b can also be written as h=50+12d 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.

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