Find a Parametrization That Gives the Same Graph as the Given

question 22

Multiple Choice

Find a parametrization that gives the same graph as the given equation. $$y = \ln x ^ { 5 }$$

• A) \(x = t ^ { 3 } , y = t ^ { 15 }\)
• B) \(x = e ^ { t } , y = \frac { t } { 5 }\)
• C) \(x = \frac { t } { 5 } , y = e ^ { t }\)
• D) \(x = t ^ { 15 } , y = t ^ { 3 }\)
• E) \(x = e ^ { t } , y = 5 t\)

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Definitions:

Convex Preferences

A characteristic of consumer preference whereby a consumer prefers combinations or mixtures of goods over extreme amounts of single goods, displaying a preference for diversification.

Indifference Curve

A graph showing a combination of two goods that give a consumer equal satisfaction and utility, demonstrating the consumer's preference.

Optimal Consumption

The most efficient allocation of resources and consumption choices based on individual preferences, maximizing utility.

Utility Function

A representation of how a consumer ranks different bundles of goods according to their level of satisfaction or utility.