Hooke's Law States That the Force $F$ Required to Compress or Stretch a Spring (Within Its Elastic

question 7

Multiple Choice

Hooke's Law states that the force $F$ required to compress or stretch a spring (within its elastic limits) is proportional to the distance $d$ that the spring is compressed or stretched from its original length. That is, $F = k d$ , where $k$ is the measure of the stiffness of the spring and is called the spring constant. The table below shows the elongation $d$ in centimeters of a spring when a force of $F$ kilograms is applied.
$\begin{array}{|c|c|}\hline \text { Force, } \boldsymbol{F} & \text { Elongation, } \boldsymbol{d} \\\hline 20 & 2.8 \\\hline 40 & 5.0 \\\hline 60 & 8.0 \\\hline 80 & 10.6 \\\hline 100 & 13.2 \\\hline\end{array}$

Find the equation of the line that seems to best fit the data. Use the model to estimate the elongation of the spring when a force of 50 kilograms is applied. Round your answer to one decimal place.

• A) \(13.2\) centimeters
• B) \(9.9\) centimeters
• C) \(3.3\) centimeters
• D) \(6.6\) centimeters
• E) \(5.0\) centimeters

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Definitions:

AVC (Average Variable Cost)

The cost of labor, materials, and other variable inputs divided by the quantity of output produced.

MC (Marginal Cost)

The increase in total production cost that comes from making or producing one additional unit of a product or service, a concept critical in economic theory for determining the optimal production level.

Shutdown Point

The level of production and price where a firm's total revenue just covers its variable costs, below which it would cease operations.

AVC (Average Variable Cost)

The total variable cost divided by the number of units produced, indicating the variable cost per unit.