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The 2005 to 2015 population density of a...

The 2005 to 2015 population density of a certain town can be modeled by the equation `d =21.3y +1,927.3`, where y represents the number of years since 2005 and d represent the population density .Which of the following best describes the meaning of the number 21,3 in the equation?

A

The estimated difference between the population density in 2005 and 2015.

B

The estimated increase in the population density each year.

C

The population density in 2005

D

The total population in 2005

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding the meaning of the number 21.3 in the equation \( d = 21.3y + 1927.3 \), we can break it down step by step. ### Step 1: Understand the equation The equation models the population density \( d \) of a town from 2005 to 2015. Here, \( y \) represents the number of years since 2005. ### Step 2: Identify the components of the equation In the equation \( d = 21.3y + 1927.3 \): - \( 1927.3 \) represents the initial population density in the year 2005 (when \( y = 0 \)). - \( 21.3 \) is the coefficient of \( y \), which indicates how the population density changes as the years increase. ### Step 3: Interpret the coefficient 21.3 The coefficient \( 21.3 \) indicates the rate of change of the population density per year. This means that for each additional year after 2005, the population density increases by \( 21.3 \) units. ### Step 4: Conclusion Thus, the number \( 21.3 \) in the equation represents the rate of increase of the population density per year. ### Final Answer The number \( 21.3 \) represents the rate of increase of population density per year. ---
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