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A Cocoa Catastrophe

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Chocolate is made from a crop called cocoa, which grows on a tree. Cocoa trees are vulnerable to extreme weather events such as floods and droughts, which means that more and more cocoa trees do not successfully produce cocoa each year. 

The number of cocoa trees in a plantation that are still producing cocoa is given by

\[C = 16500\ \times {0.82}^{n}\]

where \(n\) is the number of years after the cocoa trees are first planted.

a) Write down the number of cocoa trees first planted.

[1 mark]

b) Write down the annual percentage decrease of cocoa trees.

[2 marks]

c) Show that the number of successful cocoa trees after 4 years is less than half the number of trees first planted.

[2 marks]

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