At time = 0 hours a tank is full of water. Water leaks from the tank. At the end of every hour there is 2% 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 $V_t$. Given that $V_0 = 2000$ $V_{t-1} = kV_t$, write down the value of k.

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At time = 0 hours a tank is full of water - Edexcel - GCSE Maths - Question 18 - 2017 - Paper 2

Question 18

At time = 0 hours a tank is full of water. Water leaks from the tank. At the end of every hour there is 2% less water in the tank than at the start of the hour. The ... show full transcript

Worked Solution & Example Answer:At time = 0 hours a tank is full of water - Edexcel - GCSE Maths - Question 18 - 2017 - Paper 2

Step 1

write down the value of k

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Answer

Since the tank loses 2% of its water each hour, 98% of the water remains after every hour. Hence, the relationship between the volumes can be expressed as:

$V_t = 0.98 V_{t-1}$

This indicates that at the start of each hour, the volume of water is multiplied by 0.98. Therefore, we find:

$k = 0.98$ .

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