Use the equation from part ​a) to set up an inequality. Solve the inequality to find the number of years after 2015 in which the percentage will occur. Then use that value to find the year. The equation is s=-2.0t+33.6 

To solve this problem, let's break it down step by step.

1. **Given equation**:  
   The equation from part (a) is:  
   \[
   s = -2.0t + 33.6
   \]
   where:
   - \( s \) is the percentage
   - \( t \) is the number of years after 2015

2. **Setting up the inequality**:  
   Let's assume we are asked to find when the percentage \( s \) is less than or equal to a certain value. For example, if you want to find when \( s \leq 20\% \), we set up the inequality as follows:  
   \[
   -2.0t + 33.6 \leq 20
   \]

3. **Solve the inequality**:
   \[
   -2.0t + 33.6 \leq 20
   \]
   First, subtract 33.6 from both sides:  
   \[
   -2.0t \leq 20 - 33.6
   \]
   \[
   -2.0t \leq -13.6
   \]
   Now, divide both sides by -2.0. (Remember to flip the inequality sign when dividing by a negative number):  
   \[
   t \geq \frac{-13.6}{-2.0}
   \]
   \[
   t \geq 6.8
   \]

4. **Finding the year**:  
   Since \( t \) represents the number of years after 2015, we calculate:  
   \[
   \text{Year} = 2015 + 6.8 \approx 2022
   \]
   So, the percentage will occur around the year **2022**.

---

Would you like any details on the steps above, or do you have any questions?

Here are 5 related questions:
1. What would the year be if the inequality was \( s \geq 25 \% \)?
2. How does the slope of the equation affect the percentage change over time?
3. What happens if the percentage is projected to be less than 10%? In which year would that happen?
4. Can you graph the equation and interpret the trend over time?
5. How would a different starting year (say, 2010) change the outcome of this inequality?

**Tip**: Always remember to flip the inequality sign when multiplying or dividing by a negative number in inequalities.

Use the equation from part ​a) to set up an inequality. Solve the inequality to find the number of years after 2015 in which the percentage will occur. Then use that value to find the year. The equation is s=-2.0t+33.6.

Learn how to solve linear inequalities using the equation s = -2.0t + 33.6. Follow step-by-step instructions to set up the inequality, solve for the number of years after 2015, and determine when the percentage will reach a certain value. Suitable for high school students in Grades 9-12.

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