One year, the population of a city was 400,000. Several years later it was 340,000. Find the percent decrease.
The Correct Answer and Explanation is:
To calculate the percent decrease in the population, we need to use the following formula for percent change:
[
\text{Percent Decrease} = \frac{\text{Old Population} – \text{New Population}}{\text{Old Population}} \times 100
]
Step 1: Identify the given values
- Old Population = 400,000 (the initial population)
- New Population = 340,000 (the population after several years)
Step 2: Subtract the new population from the old population
[
\text{Decrease in Population} = 400,000 – 340,000 = 60,000
]
This means the population decreased by 60,000 people over the period.
Step 3: Calculate the percent decrease
Now, substitute the values into the formula:
[
\text{Percent Decrease} = \frac{60,000}{400,000} \times 100
]
[
\text{Percent Decrease} = 0.15 \times 100 = 15\%
]
Thus, the population decreased by 15%.
Explanation:
The calculation of percent change helps us understand the relative reduction in size or value. In this case, the decrease in the population is expressed as a percentage of the original population (400,000). We first determined how much the population decreased (60,000) and then calculated what fraction of the original population that decrease represents. Multiplying that fraction by 100 converts it into a percentage. The result, 15%, tells us that the population has decreased by 15% from its original value.
Understanding percent decreases is essential in many fields, including economics, demographics, and business, as it gives a clear idea of the proportion of change in relation to the original value. In this case, it means that, over several years, the city’s population declined by 15% from its previous size.