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PATTERNS, FUR1 2008 VCAA 9 MC

When full, a swimming pool holds 50 000 litres of water.

Due to evaporation and spillage the pool loses, on average, 2% of the water it contains each week.

To help to make up this loss, 500 litres of water is added to the pool at the end of each week.

Assume the pool is full at the start of Week 1.

At the start of Week 5 the amount of water (in litres) that the pool contains will be closest to

A.   `47\ 500`

B.   `47\ 600`

C.   `48\ 000`

D.   `48\ 060`

E.   `48\ 530` 

Show Answers Only

`D`

Show Worked Solution

`text(Let)\ \ V_n=\ text(Volume at the start of week)\ n`

`V_1=50\ 000`

♦ Mean mark 41%.

`V_2=(50\ 000)0.98+500 =49\ 500`

`V_3=(49\ 500)0.98+500 =49\ 010`

`V_4=(49\ 010)0.98+500 =49\ 529.8`

`V_5=(48\ 529.8)0.98+500=48\ 059.2…`

`=>D`

Filed Under: APs and GPs - MC

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