Determine Whether the Linear Transformation T Is One-To-One and Whether $5 \%$

question 72

Multiple Choice

Determine whether the linear transformation T is one-to-one and whether it maps as specified.
-The population of a city in 2000 was 400,000 while the population of the suburbs of that city in 2000 was 900,000.
Suppose that demographic studies show that each year about $5 \%$ of the city's population moves to the suburbs (and $95 \%$ stays in the city) , while $4 \%$ of the suburban population moves to the city (and $96 \%$ remains in the suburbs) .
Compute the population of the city and of the suburbs in the year 2002. For simplicity, ignore other influences on the population such as births, deaths, and migration into and out of the city/suburban region.

• A) City: \(\quad 430,560\)
• Suburbs: 869,440
• B) City: \(\quad 361,000\)
• Suburbs: 939,000
• C) City: \(\quad 361,000\)
• Suburbs: 829,440
• D) City: \(\quad 416,000\)
• Suburbs: 884,000

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Definitions:

Initial Investment

The amount of money used to start a project, purchase an asset, or invest in a financial venture.

Coefficient of Variation

A standardized measure of dispersion of a probability distribution or frequency distribution, often expressed as a percentage.

Variance

A measure of the dispersion or spread of a set of data points around their mean value.

Minimin Strategy

A decision rule used in scenarios involving uncertainty, where the decision maker aims to minimize the potential for the worst-case scenario.