Question Calculate the percentage decrease in a town's population, given the population was 15600 in 1990 and is now 11420.

Studdy Solution

STEP 1

Assumptions
1. The population of the town in the year 1990 was 15,600.
2. The current population of the town is 11,420.
3. We are looking to calculate the percentage decrease in the population from 1990 to the current year.

STEP 2

First, we need to find the absolute decrease in population. We can do this by subtracting the current population from the population in 1990.
$\text{Decrease in population} = \text{Population in 1990} - \text{Current population}$

STEP 3

Now, plug in the given values for the population in 1990 and the current population to calculate the decrease in population.
$\text{Decrease in population} = 15,600 - 11,420$

STEP 4

Calculate the decrease in population.
$\text{Decrease in population} = 15,600 - 11,420 = 4,180$

STEP 5

Next, we need to calculate the percentage decrease in population. The percentage decrease is given by the formula:
$\text{Percentage decrease} = \left(\frac{\text{Decrease in population}}{\text{Population in 1990}}\right) \times 100\%$

STEP 6

Plug in the values for the decrease in population and the population in 1990 to calculate the percentage decrease.
$\text{Percentage decrease} = \left(\frac{4,180}{15,600}\right) \times 100\%$

STEP 7

Calculate the fraction.
$\text{Percentage decrease} = \left(\frac{4,180}{15,600}\right) \times 100\% \approx 0.2679 \times 100\%$

STEP 8

Finally, convert the decimal to a percentage.
$\text{Percentage decrease} \approx 0.2679 \times 100\% = 26.79\%$
The percentage decrease in the population is approximately 26.79%.

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