Economics Unit on Cost and Equations

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Questions and Answers

What is the marginal cost of producing one additional unit?

  • x + 1000
  • 2x
  • $2 (correct)
  • $1000

What does the y-intercept of the line represent?

  • The variable cost of production
  • The fixed cost of production (correct)
  • The total cost of production
  • The cost of producing one unit

If the manufacturer produces 100 units, what is the total cost?

  • $1000
  • $2000
  • $2200 (correct)
  • $1200

What is the economic significance of the slope of the line?

<p>The marginal cost (D)</p> Signup and view all the answers

What is the fixed cost of production?

<p>$1000 (B)</p> Signup and view all the answers

What does the slope of the equation $y = 30,000 - 400t$ represent in the context of the oil tank example?

<p>The daily decrease in the amount of oil in the tank (A)</p> Signup and view all the answers

What does the y-intercept of the equation $y = 500,000 - 50,000x$ represent in the context of the equipment depreciation example?

<p>The original value of the equipment when it was purchased (B)</p> Signup and view all the answers

If the equation $y = 30,000 - 400t$ represents the amount of oil in the tank, how many gallons of oil will be left after 10 days?

<p>26,000 gallons (B)</p> Signup and view all the answers

What is the slope of a line perpendicular to the line represented by the equation $y = 500,000 - 50,000x$?

<p>1/50,000 (A)</p> Signup and view all the answers

If the value of a piece of equipment is given by the equation $y = 500,000 - 50,000x$, what will its value be after 5 years?

<p>$250,000 (B)</p> Signup and view all the answers

What is the slope of the line whose equation is 2x + 3y = 6?

<p>-2/3 (D)</p> Signup and view all the answers

What is the y-intercept of the line whose equation is 2x + 3y = 6?

<p>(0, 2) (A)</p> Signup and view all the answers

What is the slope of the line that passes through the point (2, 1) and has a slope of 3?

<p>3 (A)</p> Signup and view all the answers

Which of the following statements is TRUE about the line that passes through the point (2, 1) and has a slope of 3? (Select all that apply)

<p>The line has a positive slope. (A), The line has a steep upward trend. (B)</p> Signup and view all the answers

What is the equation of the line passing through the points (1,2) and (3,4)?

<p>y = x + 1 (D)</p> Signup and view all the answers

What is the slope of the line passing through the points (-2, 3) and (4, -1)?

<p>-2 (B)</p> Signup and view all the answers

Find the equation of the line passing through the point (2, -1) with a slope of -3, in point-slope form.

<p>y + 1 = -3(x - 2) (A)</p> Signup and view all the answers

What is the equation for a horizontal line that passes through the point (-3, 5)?

<p>y = 5 (B)</p> Signup and view all the answers

Which equation represents a line passing through the points (2, -4) and (2, 3)?

<p>x = 2 (B)</p> Signup and view all the answers

What is the slope of the line passing through (5, 3) and parallel to the line 2x + 5y = 7?

<p>-2/5 (B)</p> Signup and view all the answers

What is the equation of the line passing through (-4, 8) and perpendicular to the line y = 2/5x + 2 in point-slope form?

<p>y - 8 = -5/2(x + 4) (D)</p> Signup and view all the answers

What is the temperature at noon (t = 0) if the temperature T(t) = -3t + 50 describes the temperature drop in a city?

<p>50°F (B)</p> Signup and view all the answers

What is the rate of change of the temperature in the city described in Example #11?

<p>-3°F (C)</p> Signup and view all the answers

Given a line in standard form Ax + By = C (where A, B, and C are constants), what is its slope?

<p>-A/B (C)</p> Signup and view all the answers

What does the 0.03 represent in the function $C(x) = 0.03x + 5$?

<p>The percentage (as a decimal) of the purchase price of the book charged for shipping (D)</p> Signup and view all the answers

What is the shipping and handling charge for a book order that costs $20?

<p>$5.60 (C)</p> Signup and view all the answers

If the shipping and handling charge for a book order is $7.25, what is the purchase price of the book order?

<p>$25 (C)</p> Signup and view all the answers

What is the cost of shipping and handling for a book order that costs $100?

<p>$8.00 (D)</p> Signup and view all the answers

Flashcards

Slope of a line

The measure of how steep a line is on a graph, calculated as rise over run.

Y-intercept

The point where the line crosses the y-axis, represented as (0, y).

Equation of a line

A mathematical representation of a line, typically in the form y = mx + b.

Finding slope from equation

To find slope, rearrange equation into slope-intercept form y = mx + b.

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Rise over run

A way to express slope as the vertical change (rise) divided by the horizontal change (run).

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Marginal Cost

The cost to produce one additional unit of production.

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Slope of Cost Function

The slope of the cost function represents the marginal cost, indicating cost increase per unit produced.

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Fixed Costs

Costs that do not change with the amount of goods produced, represented by the y-intercept.

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Economic Significance of Slope

Indicates the increase in cost associated with producing one more unit, here it’s $2 per unit.

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Slope

The change in y-value over the change in x-value, showing rate of change.

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Depreciation

The reduction in value of an asset over time due to wear and tear.

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Point-Slope Form

A formula for a line using a known point and slope: y - y1 = m(x - x1).

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Parallel Lines

Lines that have the same slope and never intersect.

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Slope Formula

The formula to calculate slope between two points: m = (y2 - y1) / (x2 - x1).

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Slope-Intercept Form

An equation of a line in the form y = mx + b where m is the slope and b is the y-intercept.

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Horizontal Line Equation

The equation of a line that runs horizontally, with a constant y-value: y = b.

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Finding temperature function

The temperature can be expressed as T(t) = -3t + 50 based on hourly drop.

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Perpendicular lines

Lines that intersect at a right angle, slopes are negative reciprocals.

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Rate of change

Describes how one quantity changes in relation to another, like temperature drop 3°F/hour.

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Shipping and Handling Function

$C(x) = 0.03x + 5$ represents the total shipping cost dependent on book price.

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Fixed Cost in Shipping

The constant $5 in the shipping function, regardless of book price.

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Variable Cost in Shipping

The $0.03 per dollar of book price added to the shipping cost.

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Total Cost Expression

The full expression for shipping and handling costs, $C(x)$.

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Percentage in Shipping Cost

3% of the purchase price represented as 0.03x in the function.

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