Questions: The population of a town increased from 3,150 people in the year 2005 to 5,150 people in 2009. Find the absolute and relative (percent) increase. Absolute increase: people Relative increase: % Round to the nearest tenth of a percent.

The population of a town increased from 3,150 people in the year 2005 to 5,150 people in 2009. Find the absolute and relative (percent) increase.

Absolute increase: people

Relative increase: %

Round to the nearest tenth of a percent.

Transcript text: The population of a town increased from 3,150 people in the year 2005 to 5,150 people in 2009 . Find the absolute and relative (percent) increase. Absolute increase: $\square$ people Relative increase: $\square$ \% Round to the nearest tenth of a percent.

Solution

Solution Steps

Step 1: Calculate the Absolute Increase in Population

To find the absolute increase in population, subtract the initial population from the final population:

\[P_{absolute} = P_{final} - P_{initial} = 5150 - 3150 = 2000\]

Step 2: Calculate the Relative (Percent) Increase in Population

To find the relative increase, divide the absolute increase by the initial population and multiply by 100 to get a percentage:

\[P_{relative} = \left(\frac{P_{final} - P_{initial}}{P_{initial}}\right) \times 100\% = \left(\frac{2000}{3150}\right) \times 100\% = 63.5\%\]

Final Answer:

The absolute increase in population from 2005 to 2009 is 2000, and the relative increase is 63.5%.

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