The median age of the U.S. population for each year t between 1970 and 2010 can be
approximated 𝐴(𝑡) = 0.243𝑡 − 450.8. (Source: U.S. Census Bureau) a. Compute the
median ages in 1980 and 2000.  What is the slope of the graph of A

The function provided for the median age of the U.S. population is:

\[
A(t) = 0.243t - 450.8
\]

### a. Compute the median ages in 1980 and 2000:

1. **For 1980:**
   \[
   A(1980) = 0.243(1980) - 450.8
   \]
   Let's calculate this:
   \[
   A(1980) = 0.243 \times 1980 - 450.8 = 481.14 - 450.8 = 30.34
   \]
   So, the median age in 1980 was approximately **30.34 years**.

2. **For 2000:**
   \[
   A(2000) = 0.243(2000) - 450.8
   \]
   Let's calculate this:
   \[
   A(2000) = 0.243 \times 2000 - 450.8 = 486 - 450.8 = 35.2
   \]
   So, the median age in 2000 was approximately **35.2 years**.

### Slope of the graph:

The slope of the linear equation \( A(t) = 0.243t - 450.8 \) is the coefficient of \( t \), which is **0.243**.

Thus, the slope of the graph is **0.243**. This means that the median age of the U.S. population increases by 0.243 years for each year that passes.

---

Would you like more details or explanations about any part of this? Here are five questions you might consider:

1. How would the equation change if the population's median age increased at a different rate?
2. What does the y-intercept (-450.8) represent in the context of this model?
3. Could you calculate the median age in 2010 using the same equation?
4. How accurate do you think a linear model like this is for projecting long-term trends in population age?
5. What happens if you try to calculate the median age for years far outside the 1970–2010 range?

**Tip:** The slope of a linear function tells you how much the output changes per unit of change in the input—this is critical for interpreting trends in real-world data.

The median age of the U.S. population for each year t between 1970 and 2010 can be approximated by A(t) = 0.243t − 450.8. Compute the median ages in 1980 and 2000. What is the slope of the graph of A?

Learn how to calculate the median age of the U.S. population in 1980 and 2000 using the linear function A(t) = 0.243t - 450.8. This solution explains how the slope affects the age increase and includes step-by-step calculations. Suitable for students in Grades 8-10.

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