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]