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Profiting from Reforestation

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A small company is planting trees in areas of the Amazon rainforest that have been affected by forest fires.

On any day, the cost to the company, $y, of planting x trees is modelled to be the sum of two elements:

  • a fixed cost
  • a cost that is proportional to the number of trees planted that day

a) Write down a general equation linking y with x for this model.

[2 marks]

The company is subsidised $2 by the government for each tree planted.

On a day when 80,000 trees are planted, the company makes a profit of £500

On a day when 30,000 trees are planted, the company makes a loss of £80

Using the above information,

b) Show that \(y =  0.84x + 428\)

[3 marks]

c) With reference to the model, interpret the significance of the value 0.84 in the equation.

[1 mark]

d) Find the least number of trees that must be planted on any given day for the company to make a profit that day.

[3 marks]

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