# We often use graphs of recent data to project what future data may bring

August 30, 2017

Question
(30 points) We often use graphs of recent data to project what future data may bring. The following is the graph of a car’s value.
The car was purchased for \$20,000. Each year, the car’s value decreases by \$2,800. We can use this to project what the car will be worth if we ever decide to sell the car.

Write a formula to model the car’s value, where is the value of the car and is the number of years.

What will be the value of the car after 5 years, algebraically? Does your calculation match the graph provided?

What is an appropriate label for each axis?

Estimate the and intercepts and state what each one means in relation to the value of the car.

(25 points) A phone company has two different phone plans from which you can choose.
Plan A: \$45 a month for unlimited calling

Plan B: \$15 a month plus \$0.10 a minute

Based on the information provided, solve the following problems:

What will be the cost equation for Plan A and Plan B?

Write an inequality that models the conditions. Solve the inequality to find out how many calls must be made to make Plan A the better deal. Show all your steps.

(15 points) A company that manufactures aquariums has a fixed cost of \$116,000. It costs \$150 to produce each aquarium. The selling price is \$350 per aquarium. How many aquariums does the business need to sell to break even? (15 points) Solve the following system of equations using elimination or matrices.
(15 points) Use the back substitution method to solve the given matrix. Begin by writing the corresponding linear equations, and then use the substitution method to solve for the variables.

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