Questions: Compute the absolute and relative change for the values below. Use the table to select the appropriate model for the data below. Time Value Absolute Change Relative Change 0 138.500 1 155.76 2 173.02 3 190.28 17.26 x+138.5 138.5(17.26)^t 17.26(1.385)^t 138.5(18.26)^t 138.5(x+17.26) 138.5 x+17.26

Solution Steps

To compute the absolute and relative change for the given values, we need to follow these steps:

1. Calculate the absolute change by subtracting the previous value from the current value.
2. Calculate the relative change by dividing the absolute change by the previous value and then multiplying by 100 to get a percentage.

The absolute change between consecutive values is calculated as follows:

\[ \text{Absolute Change}_1 = 155.76 - 138.5 = 17.26 \]

\[ \text{Absolute Change}_2 = 173.02 - 155.76 = 17.26 \]

\[ \text{Absolute Change}_3 = 190.28 - 173.02 = 17.26 \]

Thus, the absolute changes are:

\[ \text{Absolute Changes} = [17.26, 17.26, 17.26] \]

The relative change is calculated using the formula:

\[ \text{Relative Change} = \left( \frac{\text{Absolute Change}}{\text{Previous Value}} \right) \times 100 \]

Calculating the relative changes:

\[ \text{Relative Change}_1 = \left( \frac{17.26}{138.5} \right) \times 100 \approx 12.46 \]

\[ \text{Relative Change}_2 = \left( \frac{17.26}{155.76} \right) \times 100 \approx 11.08 \]

\[ \text{Relative Change}_3 = \left( \frac{17.26}{173.02} \right) \times 100 \approx 9.976 \]

Thus, the relative changes are:

\[ \text{Relative Changes} \approx [12.46, 11.08, 9.976] \]

Final Answer