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

Question 18

At time $t = 0$ 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.... show full transcript

Worked Solution & Example Answer:At time $t = 0$ 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

The problem states that at the end of every hour there is 2% less water in the tank. This can be expressed as:

$V_t = V_{t-1} imes (1 - 0.02) = V_{t-1} imes 0.98$

From the given equation $V_{t-1} = kV_t$ , we can rearrange it to find $k$ :

Substituting our value of $V_t$ gives:

$V_{t-1} = k imes (V_{t-1} imes 0.98)$

Thus, we can conclude:

$k = 0.98$

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