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Rates, SM-Bank 005

A tree was 143 cm tall at the beginning of January.  At the end of May it measured 233 cm tall.

  1. Calculate the average rate of growth of the tree for the 5 month period.  (2 marks)

  2. If this rate of growth were to continue, how many more months would it take the tree to reach a height of 611 cm?  (2 marks)

Show Answers Only

a.    \(18\ \text{cm}/ \text{month}\)

b.    \(21\ \text{months}\)

Show Worked Solution
a.    \(\text{Growth}\) \(=233-143\)
    \(=90\ \text{cm}\)

 

\(\text{Rate of growth}/\text{month}\) \(=\dfrac{90}{5}\ \text{cm}/\text{month}\)
  \(=18\ \text{cm}/\text{month}\)

 

b.    \(\text{Growth}\) \(=611-233\)
    \(=378\ \text{cm}\)
     
  \(\text{Months}\) \(=\dfrac{378}{18}\)
    \(=21\)

 
\(\therefore\ \text{It would take}\ 21\ \text{months for the tree to grow to a height of }\ 611\ \text{cm.}\)