Use a Graphing Calculator to Plot the Data and Find

question 293

Multiple Choice

Use a graphing calculator to plot the data and find the quadratic function of best fit.
-A small manufacturing firm collected the following data on advertising expenditures (in thousands of dollars) and total revenue (in thousands of dollars) . $\begin{array}{c|c}\text { Advertising, } \mathrm{x} & \text { Total Revenue, } \mathrm{R} \\\hline 25 & 6430 \\28 & 6432 \\31 & 6434 \\32 & 6434 \\34 & 6434 \\39 & 6431 \\40 & 6432 \\45 & 6420\end{array}$

Find the quadratic function of best fit.

• A) \(R ( x ) = - 0.015 x ^ { 2 } + 4.53 x + 6123\)
• B) \(R ( x ) = - 0.091 x ^ { 2 } + 5.95 x + 6337\)
• C) \(R ( x ) = - 0.024 x ^ { 2 } + 7.13 x + 6209\)
• D) \(R ( x ) = - 0.31 x ^ { 2 } + 2.63 x + 6128\)

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Definitions:

First Theorem of Welfare Economics

A principle stating that under certain conditions, a market in equilibrium will allocate resources efficiently in a way that maximizes total social welfare.

Competitive Equilibrium

A market state where supply equals demand, leaving no incentive for price changes as long as external conditions remain constant.

Homothetic Preferences

Preferences where if a consumer prefers a bundle of goods A to B, they will also prefer a scaled-up version of A to the same scale-up of B, maintaining the same proportions.

Marginal Rate of Substitution

How quickly a consumer agrees to trade one good for another, aiming to keep their level of pleasure steady.