Quadratic Inequalities Word Problem: the price of carbon fibre

[shaznayel]

Suppose that an engineer determines that she can use the formula -r^2+14≤P to estimate when the price of carbon fibre will be P dollars per kilogram or less in T years from the present. When will carbon fibre be available at $10/kg or less?

 

[Otis]

Suppose that an engineer determines that she can use the formula -r^2+14≤P to estimate when the price of carbon fibre will be P dollars per kilogram or less in T years from the present. When will carbon fibre be available at $10/kg or less?

The exercise has not defined symbol r, but let's assume that it is the time variable, and that symbol T represents the specific value of r which they've asked for. (In other words, T is a constant.)

Symbol P represents the price (in dollars per kilogram) at time r, and the present time is at r = 0 years from now.

The question is asking for the value of r which causes P to equal 10. In other words, we substitute P=10 and then solve this equation:

-r^2 + 14 = 10

That solution is the value of T.