Graph the Points and from Visual Inspection, Select the Model

question 28

Multiple Choice

Graph the points and from visual inspection, select the model that would best fit the data. Choose from $\begin{array} { l l } y = m x + b \text { (linear) } & y = a b ^ { x } \text { (exponential) } \\y = a + b \ln x \text { (logarithmic) } & y = \frac { c } { 1 + a e ^ { - b x } } \text { (logistic) }\end{array}$ Then use a graphing utility to find a function that fits the data. (Hint: For a logistic model, go to STAT, CALC,
Logistic.)
- $\begin{array} { c | c } x & y \\\hline 4 & 4.4 \\5 & 5.2 \\9 & 10.5 \\14 & 25.1 \\20 & 71.3 \\24 & 143.1\end{array}$

• A) \(y = - 101.2 + 61.88 \ln x\)
• B) \(y = 2.2 ( 1.19 ) ^ { x }\)
• C) \(y = \frac { 425 } { 1 + 214 e ^ { - 0.11 x } }\)
• D) \(y = 6.2 x - 35.27\)

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Definitions:

High Failure Rate

A situation where a significant proportion of attempts or efforts in a particular endeavor result in failure.

Competitive Business

A business that actively strives for a superior position in the marketplace through strategies like innovation, quality improvement, and customer service enhancement.

Challenges of Growth

The difficulties and obstacles that a company or organization faces as it expands or increases in size.

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Pertaining to a market structure where a few firms dominate the industry, often leading to limited competition.