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.
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 \(y = 0.84x + 428\)
c) With reference to the model, interpret the significance of the value 0.84 in the equation.
d) Find the least number of trees that must be planted on any given day for the company to make a profit that day.