Problem 71 - Algebra for College Students

Question

Between 2000 and \(2016,\) the estimated population of metro New Orleans, Louisiana, declined from 1,337,726 to \(1,268,883 .\) What was the percent decrease to the nearest tenth?

Step-by-Step Solution

Answer

The percent decrease is 5.2\%.

Step 1 - Identify the Initial and Final Populations

The initial population in 2000 is 1,337,726, and the final population in 2016 is 1,268,883.

Step 2 - Calculate the Decrease in Population

Subtract the final population from the initial population: \[1,337,726 - 1,268,883 = 68,843\]

Step 3 - Calculate the Decrease as a Fraction of the Initial Population

Divide the decrease in population by the initial population: \[\frac{68,843}{1,337,726} = 0.0515\]

Step 4 - Convert the Decimal to a Percentage

Multiply the result by 100 to convert it to a percentage: \[0.0515 \times 100 = 5.15\%\] To the nearest tenth, this is 5.2\%

Key Concepts

Initial Population

To calculate the percent decrease in population, we first need to understand the concept of the initial population. The initial population represents the number of people living in a particular area at the beginning of a specified time period. In this exercise, the initial population of metro New Orleans in the year 2000 is given as 1,337,726. Having a clear idea of the initial population is crucial because it serves as the reference point from which we measure any increase or decrease in population over time. This value will be used as the base in our percentage calculations.

Final Population

Next, we need to understand the final population for percent decrease calculations. The final population represents the number of people living in a particular area at the end of the specified time period. For this exercise, the final population of metro New Orleans in 2016 is given as 1,268,883. Determining the final population is essential because it shows the number of people remaining after any changes (such as decreases in population) have taken place over the specified time period. The final population will help us measure how much change has happened relative to the initial population.

Population Decrease

Now, let's focus on understanding the concept of population decrease. Population decrease is the difference between the initial population and the final population. In mathematical terms, it is calculated by subtracting the final population from the initial population. Using the numbers from the exercise:
\[ \text{Population Decrease} = 1,337,726 - 1,268,883 = 68,843 \] This means that between 2000 and 2016, the population of metro New Orleans decreased by 68,843 people. This decrease is an important value because it quantifies the change in population over the given period and helps us in calculating the percentage decrease.

Percentage Calculation

Finally, let's dive into the percentage calculation to determine the percent decrease in population. Percentage calculation involves converting a fraction or a ratio into a percentage. For calculating the percent decrease, we follow these steps:

• First, divide the population decrease by the initial population to get the decrease as a fraction: \[ \frac{68,843}{1,337,726} = 0.0515 \]
• Next, multiply the result by 100 to convert it to a percentage: \[ 0.0515 \times 100 = 5.15 \% \]
• Lastly, round the result to the nearest tenth to get the final percent decrease: \[ 5.15 \% \approx 5.2 \% \]

By following these steps, we find that the population of metro New Orleans decreased by approximately 5.2% between 2000 and 2016. This percentage quantifies the relative change, making it easier to understand and compare.