Use the information given below to write an equation in the form y = mx + b for the average cost, y, of a math text book x years after 1990. Then use the equation to predict the average cost in 2016.

Answer 1

Let's assume that the average cost of a math textbook in 1990 was $50 and that the cost has been increasing at a rate of $4 per year since then.

To find the equation in the form y = mx + b, we need to determine the slope (m) and the y-intercept (b).

Slope (m): The rate of increase in cost per year.
In this case, the rate of increase is $4 per year, so m = 4.

Y-intercept (b): The initial cost in 1990.
In this case, the initial cost is $50, so b = 50.

Therefore, the equation is:
y = 4x + 50

To predict the average cost in 2016 (x = 26 since it's 26 years after 1990), we substitute x = 26 into the equation:
y = 4 * 26 + 50
y = 104 + 50
y = 154

Therefore, the predicted average cost of a math textbook in 2016 is $154.

Answer 2

A manufacturer has total revenue given by the function R(x) = 5.80x and has total cost given by C(x) = 1.80x + 76 where x is the number of units produced and sold.

How many units must be produced to break-even?

Answer 3

To break-even, the total revenue (R) must be equal to the total cost (C). We can set up the equation:

R(x) = C(x)

Substituting the given revenue and cost functions:

5.80x = 1.80x + 76

Now we can solve for x:

5.80x - 1.80x = 76

4x = 76

Dividing both sides of the equation by 4:

x = 76 / 4

x = 19

Therefore, 19 units must be produced to break-even.