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.

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.