Question

synthesis

1. how can percentages help us make sense of how a price has changed over time?

use the table if it helps you explain your thinking.

Explanation:

Step1: Calculate percentage change formula

The formula for percentage change is \(\text{Percentage Change}=\frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\times100\%\)

Step2: Calculate percentage change for Mattress

For Mattress: Old Value (\(2000\)) = \(995\), New Value (\(2022\)) = \(1050\)
\(\text{Percentage Change}=\frac{1050 - 995}{995}\times100\%=\frac{55}{995}\times100\%\approx5.53\%\)

Step3: Calculate percentage change for Monthly Rent

For Monthly Rent: Old Value (\(2000\)) = \(602\), New Value (\(2022\)) = \(1128\)
\(\text{Percentage Change}=\frac{1128-602}{602}\times100\%=\frac{526}{602}\times100\%\approx87.38\%\)

Step4: Calculate percentage change for Minimum Wage

For Minimum Wage: Old Value (\(2000\)) = \(5.15\), New Value (\(2022\)) = \(7.25\)
\(\text{Percentage Change}=\frac{7.25 - 5.15}{5.15}\times100\%=\frac{2.1}{5.15}\times100\%\approx40.78\%\)

Step5: Analyze the meaning of percentage change

Percentages help us standardize the comparison. A positive percentage change indicates an increase. For example, the mattress price increased by approximately \(5.53\%\), meaning it grew a relatively small amount compared to its original value. The monthly rent had an \(87.38\%\) increase, showing a large growth relative to its 2000 value. The minimum - wage increase of about \(40.78\%\) shows a moderate growth relative to its starting point in 2000.

Answer:

Percentages standardize the comparison of price changes. By calculating \(\frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\times100\%\), we can see relative growth/decline. For the mattress (\(\approx5.53\%\) increase), rent (\(\approx87.38\%\) increase), and minimum - wage (\(\approx40.78\%\) increase) in the table, percentages show how much each has grown relative to its 2000 value.