Question

The bar graph to the left shows the percentage of the U.S. population that was​ foreign-born for each decade of the twentieth century. The​ percentage, P, of the U.S. population that was​ foreign-born x years after 1900 can be modeled by the​ formula:
P​ = 0.0021xsquaredminus0.286xplus16.28
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Part 1
a. According to the​ model, what percentage of the U.S. population was​ foreign-born in 1970​?
  
enter your response here​% ​(Type an integer or a decimal. Round to one decimal place as​ needed.)

Answer 1

To find the percentage of the U.S. population that was foreign-born in 1970 using the given model \( P = 0.0021x^2 - 0.286x + 16.28 \), we first need to determine the value of \( x \), which represents the number of years after 1900.

For 1970, \( x = 1970 - 1900 = 70 \).

Now, we can substitute \( x = 70 \) into the model:

\[
P = 0.0021(70^2) - 0.286(70) + 16.28
\]

Calculating each term:

1. \( 70^2 = 4900 \)
2. \( 0.0021(4900) = 10.29 \)
3. \( 0.286(70) = 20.02 \)

Now substitute these values into the equation:

\[
P = 10.29 - 20.02 + 16.28
\]

Now, calculate \( P \):

\[
P = 10.29 - 20.02 + 16.28 = 10.29 - 20.02 + 16.28 = 6.55
\]

Therefore, the percentage of the U.S. population that was foreign-born in 1970 was approximately:

\[
P \approx 6.6\% \quad (\text{rounded to one decimal place})
\]

So, the final answer is: **6.6%**.