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At time t = 0 hours, a tank contains 2000 litres of water.
Water leaks from the tank.
At the end of every hour there is x% less water in the tank,
than at the start of the hour.
The volume of water, in litres, in the tank at time t hours is V.
Given that
V = k'V
V. = 1714.75
work out the value of k and the value of x.​

At Time T 0 Hours A Tank Contains 2000 Litres Of WaterWater Leaks From The TankAt The End Of Every Hour There Is X Less Water In The Tankthan At The Start Of Th class=

Sagot :

cairde

Answer:

k= 0.95

x = 5

Step-by-step explanation:

V₀=2000 because at the start (when t=0), there's 2000l in the tank.

V[tex]_{t}[/tex]=[tex]k^{t}[/tex]V₀

V[tex]_{t}[/tex]=2000[tex]k^{t}[/tex]

V₃=1714.75=2000k³

k³=0.857375

k= 0.95

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V[tex]_{t}[/tex]=2000[tex]k^{t}[/tex]

V[tex]_{t}[/tex]=2000[tex](0.95^{t})[/tex]

V₁=2000(0.95)=1900

So from V₀ to V₁, the tank loses 100l, which is 5% of it's volume at the start of the hour (100/2000=5%). Therefore x = 5

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