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.
