Question

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

[AI-generated answer — Bot GPT 3.5]

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

[AI-generated answer — Bot GPT 3.5]

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.

Answer 4

[AI-generated answer — Step-by-Step Bot]

To write the equation in the form y = mx + b, we need to determine the values of m and b.

Given information:
- We are looking at the average cost, y, of a math textbook x years after 1990.
- We need to predict the average cost in 2016.

Let's first determine the slope, m, which represents the rate of change in the average cost per year.

Given that the year 1990 corresponds to x = 0, we can determine the change in the average cost over x years using the given information. Let's assume the average cost in 1990 is c0.

The change in average cost over x years can be represented as:
Change in average cost = y - c0

We are not given specific values, so let's represent the change in average cost as Δy and the change in years as Δx.

Δy = y - c0
Δx = x - 0

Now, we can calculate the slope using the formula:
m = Δy / Δx

Next, let's determine the y-intercept, b, which represents the average cost at the start (when x = 0). We are given that the year is 1990, so we can assign y(0) = c0.

Now, we can write the equation in the form y = mx + b as:
y = mx + c0

Finally, we can use the equation to predict the average cost in 2016 by substituting x = 2016 - 1990 = 26 into the equation.

Please provide specific values for c0, the average cost in 1990, and any other relevant information so that we can complete the calculation accurately.