## A Cocoa Catastrophe

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]

## Decreasing Fish Stocks

Global warming will affect the world’s annual fishing catch.

In a world heated by a global warming of 2°C, the annual fishing catch will decrease by 3.3 million tonnes.

In a world heated by a global warming of 1.5°C, the annual fishing catch will decrease by 1.5 million tonnes.

Express the reduction of the annual fishing catch in a world warmed by 2°C as a fraction of the reduction in annual fishing catch in a world warmed by 1.5°C.

Given that all dimensions are given in metres, and the total area of the plot is 65㎡ , find the values of $$x$$ and $$y$$ and hence the depth and width of the shed that they need to purchase.