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PATTERNS, FUR 1 2006 VCAA 9 MC

A healthy eating and gym program is designed to help football recruits build body weight over an extended period of time.

Roh, a new recruit who initially weighs 73.4 kg, decides to follow the program.

In the first week he gains 400 g in body weight.

In the second week he gains 380 g in body weight.

In the third week he gains 361 g in body weight.

 If Roh continues to follow this program indefinitely, and this pattern of weight gain remains the same, his eventual body weight will be closest to

A.   `74.5\ text(kg)`

B.   `77.1\ text(kg)`

C.   `77.3\ text(kg)`

D.   `80.0\ text(kg)`

E.   `81.4\ text(kg)`

Show Answers Only

`E`

Show Worked Solution

`text(Checking for a common ratio,)`

♦♦ Mean mark 33%.
`t_2/t_1` `=380/400=0.95`
`t_3/t_2` `=361/380=0.95`
`:.\ text(GP where)\ \ \ a` `=400, and`
`r` `=0.95`

 

`text(S)text(ince)\ \ |\ r\ |<1,`

`S_oo` `=a/(1-r)`
  `=400/(1-0.95)`
  `=8000\ text(g)`

 

`:.\ text(Net weight gain will be 8 kg which will make Roh’s)`

`text{eventual weight  73.4 + 8 = 81.4 kg.}`

`rArr E`

Filed Under: APs and GPs - MC Tagged With: Band 6

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