Water is leaking from a tank. The volume of water in the tank after 1 hour is 100L and after 5hours the volume is 20L. Assuming the relationship is linear, find a rule and then state the initial volume of water in the tank.
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To solve , let V be the volume of water in the tank. And, let t be number of hours that the water was leaking.
So the given values of t and V are:
t V
1 100
5 20
If we express them as order pairs, it would be (1,100) and (5,20).
Now that we have our two points, determine the slope of the line connecting them. So, apply the formula:
`m=(y_2-y_1)/(x_2-x_1)`
For our problem, it will be:
`m=(V_2-V_1)/(t_2-t_1) `
`m=(20-100)/(5-1)=(-80)/4=-20`
Hence, the slope of the line is -20.
Then, use the point-slope form to get the equation.
`y - y_1 =m(x - x_1)`
For our problem, it will be:
`V-V_1=m(t - t_1)`
`V-100=-20(t-1)`
`V-100=-20t+20`
Then, isolate the V.
`V=-20t+20+100`
`V=-20t+120`
Therefore, the volume of water that remains inside the tank when the water was leaking for t hours can be determined using the equation
`V=-20t +120` .
To solve for the initial amount of water in the tank, plug-in t=0 to the equation.
`V=-20(0)+120 = 0+120=120`
Thus, the initial volume of water in the tank is 120L.
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