Graph the Points and from Visual Inspection, Select the Model

question 39

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.)
- $\begin{array}{c|c}x & y \\\hline 10 & 41.2 \\20 & 47.5 \\30 & 51.2 \\40 & 53.8 \\50 & 55.9 \\60 & 57.5\end{array}$

• A) \(y = 0.31 x + 40.3\)
• B) \(y = \frac { 138 } { 1 + 0.23 e ^ { - 0.09 x } }\)
• C) \(y = 40.8 ( 1.01 ) ^ { x }\)
• D) \(y = 20.2 + 9.11 \ln x\)

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Definitions:

Tertiary Amine

An amine where the nitrogen atom is connected to three alkyl or aryl groups.

Ethanol

Ethanol, also known as ethyl alcohol, is a volatile, flammable, colorless liquid commonly used as a psychoactive drug in alcoholic beverages and as a solvent in the chemical industry.

Metabolic Oxidation

The process in which organic substances are broken down to produce energy in cells.

Carboxylic Acids

Organic compounds containing a carboxyl group (-COOH) that are characterized by their acidic properties.