What are two ways the graphed function could be used to solve real world problems?

a) Determine an equation for the population with respect to the number of years after 2014, assuming that the population increases at a constant rate.

Solution

The function will be of the form

p=a r n, where a is the initial population, r is the rate of increase, n is the time in years and

p is the population.

p=584,513 (1.0002) n

b) Find the optimum price for the chips to maximize the profit for the company.

Solution

This will be the vertex of the function. We will need to complete the square. P=-54x2+15x+200

P=-54 (x2-12x) + 200

P=-54 (x2-12x+36-36) + 200

P=-54 (x-6) 2+45+200

P=-54 (x-6)

2+245

The optimum price is $6 per bag.