solve: units of oxygen produced = age2 - 5 x age - 50

Question

Scientists have found a mathematical model that can calculate the amount of oxygen produced by a tree. It is modelled as the quadratic: Units of oxygen produced = age2 - 5 x age - 50. Where age is measured in years. When the tree dies, oxygen production = 0. According to the model, how old are these trees when they die? Justify you answer with solution and working.

Answer 1

Let variable a represent age: a²-5a-50 is the expression for the model’s oxygen production.

When a²-5a-50=0=(a-10)(a+5), so a=10 years when production of oxygen=0 (because a>0).

The trees live to be 10 years old.