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PATTERNS, FUR1 2015 VCAA 7 MC

A plant was 80 cm tall when planted in a garden.

After it was planted in the garden, its height increased by 16 cm in the first year.

It grew another 12 cm in the second year and another 9 cm in the third year.

Assuming that this pattern of geometric growth continues, the plant will grow to a maximum height of

A.     `64\ text(cm)`

B.   `128\ text(cm)`

C.   `144\ text(cm)`

D.   `320\ text(cm)`

E.   `400\ text(cm)`

Show Answers Only

`C`

Show Worked Solution

`text(16, 12, 9, …)`

♦ Mean mark 48%.
`text(GP where)\ \ \ a` `=16, and`
`r` `=t_2/t_1=12/16=0.75`

 

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

`S_∞` `= a/(1 – r)`
  `= 16/(1 – 0.75)`
  `= 64`
`:.\ text(Max. height)` `= 80 + 64`
  `= 144`

`=> C`

Filed Under: APs and GPs - MC Tagged With: Band 5

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