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.

To compute the median ages in 1980 and 2000 using the given formula \( A(t) = 0.243t - 450.8 \), we need to substitute the values of \( t = 1980 \) and \( t = 2000 \) into the equation.

### 1. Median Age in 1980:
\[
A(1980) = 0.243 \times 1980 - 450.8
\]

Let's calculate:

\[
A(1980) = 0.243 \times 1980 - 450.8 = 480.14 - 450.8 = 29.34
\]

So, the median age in 1980 was approximately **29.34 years**.

### 2. Median Age in 2000:
\[
A(2000) = 0.243 \times 2000 - 450.8
\]

Let's calculate:

\[
A(2000) = 0.243 \times 2000 - 450.8 = 486 - 450.8 = 35.2
\]

So, the median age in 2000 was approximately **35.2 years**.

### Summary:
- **Median age in 1980**: 29.34 years
- **Median age in 2000**: 35.2 years

Would you like further details or have any other questions?

Here are five related questions to expand on this topic:
1. What is the median age in 1990 using the same formula?
2. How would you interpret the change in median age between 1980 and 2000?
3. What would be the predicted median age in 2010 based on this model?
4. How does the slope of the function \( A(t) \) relate to the change in median age over time?
5. How would you calculate the year when the median age would reach 40 years using this formula?

**Tip:** In linear models like this one, the coefficient of \( t \) (in this case, 0.243) represents the rate of change per year.

Learn how to compute the median ages in 1980 and 2000 using the linear function A(t) = 0.243t - 450.8. Detailed calculations show that the median age in 1980 was approximately 29.34 years, and in 2000, it was approximately 35.2 years. Suitable for high school students studying linear functions.

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