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Question
A family is using Liquefied petroleum gas (LPG) of weight 14.2 kg for consumption. (Full weight 29.5kg includes the empty cylinders tare weight of 15.3kg.). If it is used with constant rate then it lasts for 24 days. Then the new cylinder is replaced. Draw the graph for first 96days
Solution
The relation connecting the quantity of gas to the number of days of consumption is
y = `- 71/120 x + 14.2`
Let f(x) = `- 71/120 x + 14.2`
Here f(x) is a periodic function of period 24
∴ f(x + 24) = f(x)
When x = 0
f(0) = `- 71/120 xx 0 + 14.2`
⇒ y = 14.2
The corresponding point is (0, 14.2)
When x = 24
f(24) = `- 71/120 xx 0 + 14.2`
⇒ y = 14.2
⇒ f(24) = `- 71/5 + 14.2`
= – 14.2 + 14.2 = 0
⇒ y = 0
Corresponding point is (24 , 0)
When x = 48
f(48) = f(24 + 24 + 0)
= f(24 + 0)
= f(0) = 0
Corresponding point is (48, 0)
When x = 72
f(72) = f(24 + 24 + 24 + 0)
= f(24 + 24 + 0)
= f(24 + 0)
= f(0) = 0
Corresponding point is (72, 0)
The required graph is
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