The average consumption per person per year of whole milk can be approximated by the equation w equals negative 1.9 t plus 70.1 where t is the number of years after 1995 and w is measured in pounds. The consumption of whole milk is shown on the graph in blue. Determine when the consumption of whole milk will be less than 40 pounds per person per year.

The given equation is:

\[
w = -1.9 \cdot t + 70.1
\]

where:
- \( w \) is the consumption of whole milk in pounds per person per year.
- \( t \) is the number of years after 1995.

We need to determine when the consumption \( w \) will be less than 40 pounds per person per year. Therefore, we set up the inequality:

\[
-1.9 \cdot t + 70.1 < 40
\]

To solve for \( t \):

1. Subtract 70.1 from both sides:

\[
-1.9 \cdot t < 40 - 70.1
\]

\[
-1.9 \cdot t < -30.1
\]

2. Divide both sides by -1.9. Remember, when dividing by a negative number, the inequality sign flips:

\[
t > \frac{-30.1}{-1.9}
\]

Now, let's calculate the value:

\[
t > \frac{30.1}{1.9} \approx 15.8
\]

Since \( t \) represents the number of years after 1995, we round up to the next whole number, because time in years should be an integer.

\[
t = 16
\]

So, the consumption of whole milk will be less than 40 pounds per person per year approximately 16 years after 1995.

\[
1995 + 16 = 2011
\]

**Conclusion:** The consumption of whole milk will drop below 40 pounds per person per year starting from the year 2011.

Would you like more details or have any questions? 

Here are some related questions:

1. What will be the consumption of whole milk in the year 2020?
2. How would the result change if the threshold was 30 pounds instead of 40 pounds?
3. What does the slope \(-1.9\) represent in this context?
4. How would an increase in whole milk popularity affect the equation?
5. Can this model predict future milk consumption accurately? Why or why not?

**Tip:** When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number.

Learn how to determine when the consumption of whole milk drops below 40 pounds per person per year using a linear equation approximation. Understand the application of inequalities in solving real-world consumption problems. Suitable for students in Grades 7-9.

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