To determine the percent rate of change, we need to examine how the values change from the initial to the final point.
Here's a step-by-step outline of how to calculate the percent rate of change:
1. Identify the initial and final values:
- Initial value ([tex]\( y \)[/tex] when [tex]\( x = -3 \)[/tex]): 192
- Final value ([tex]\( y \)[/tex] when [tex]\( x = 1 \)[/tex]): 0.75
2. Calculate the absolute change:
[tex]\[
\text{Change} = \text{Final Value} - \text{Initial Value} = 0.75 - 192 = -191.25
\][/tex]
3. Calculate the percent rate of change:
[tex]\[
\text{Percent Rate of Change} = \left( \frac{\text{Change}}{\text{Initial Value}} \right) \times 100
\][/tex]
Substituting the values:
[tex]\[
\text{Percent Rate of Change} = \left( \frac{-191.25}{192} \right) \times 100
\][/tex]
4. Simplify the calculation:
[tex]\[
\text{Percent Rate of Change} = -0.99609375 \times 100
\][/tex]
[tex]\[
\text{Percent Rate of Change} = -99.609375\%
\][/tex]
Given that the percent rate of change is [tex]\(-99.609375\%\)[/tex], this is very close to a complete decrease but not exceeding 100%.
Considering the choices:
- [tex]$75 \%$[/tex] decrease
- [tex]$75 \%$[/tex] increase
- [tex]$25 \%$[/tex] decrease
- [tex]$25 \%$[/tex] increase
None of these provide the correct percent rate of change directly. However, we know from our calculations that:
- The change is a significant decrease, specifically \(-99.609375\%$.
So, the correct choice, stating a very high rate of decrease (almost 99.6%), is indirectly none of these provided options. Instead, the nearest interpretation given typical contexts would imply a substantial decrease, far more than 75%. However, it's important to acknowledge that if provided choices fit better granularity, you should select the closest one that matches calculated percent change precisely unless instructed to select only from given options.
Informed by the computed decrement, more precise answers should be included in practical scenarios.
