Data regarding the growth of a certain tree has shown that the tree grows to a height of 180\displaystyle {180} cm\displaystyle {c}{m} after one year. The data further reveals that during the next year, the height increases by 25\displaystyle {25} cm\displaystyle {c}{m}. In each successive year, the height increases by 1011\displaystyle \frac{{10}}{{11}} of the previous year's increase in height. The table below is a summary of the growth of the tree up to the end of the fourth year.

  First Year Second Year Third Year Fourth Year
Three Height(cm\displaystyle {c}{m}) 180 205 227.73 248.39
Growth (cm\displaystyle {c}{m})   25 22.73 20.66

Determine the increase in the height of the tree during the seventh year.

Formula

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Stocktake

Type in the list of known variables, example x=1,y=2...:

 

Substitute

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Solve

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(2)

Calculate the height of the tree after 8 years.

Formula

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Stocktake

Type in the list of known variables, example x=1,y=2...:

 

Substitute

   (use subscripts if necessary in this step)

Solve

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The height of the tree after 8 years  cm\displaystyle {c}{m}.

     

 (3)

Show that the tree will never reach a height of more than 455cm\displaystyle {455}{c}{m}.

Formula

   (ignore subscripts in this step but not in written work)

Stocktake

Type in the list of known variables, example x=1,y=2...:

 

Substitute

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Solve


   (use subscripts if necessary in this step)

The maximum height the tree will ever reach is cm\displaystyle {c}{m}.

     

(3)

[8]

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