QuestionFind the foreign-born percentage, P, in 1990 using $P=0.0021 x^{2}-0.286 x+16.28$ . Does it overestimate or underestimate?

Studdy Solution

STEP 1

Assumptions1. The percentage of the U.S. population that was foreign-born $x$ years after1900 can be modeled by the formula $=0.0021 x^{}-0.286 x+16.28$ . . We are asked to find the percentage of the U.S. population that was foreign-born in1990.
3. We are also asked to compare the model's prediction with the actual number displayed on the graph.

STEP 2

First, we need to find the value of $x$ for the year1990. Since $x$ represents the years after1900, we can calculate $x$ as follows $x =1990 -1900$

STEP 3

Calculate the value of $x$ .
$x =1990 -1900 =90$

STEP 4

Now, we can substitute $x =90$ into the model to find the percentage of the U.S. population that was foreign-born in1990.
$=0.0021 \times90^{2} -0.286 \times90 +16.28$

STEP 5

Calculate the value of $$.
$=0.0021 \times90^{2} -0.286 \times90 +16.28 =8.9$ So, according to the model,8.9% of the U.S. population was foreign-born in1990.

STEP 6

Next, we need to compare the model's prediction with the actual number displayed on the graph. Since the actual problem does not provide the graph, we will assume that the actual number displayed on the graph is $_{actual}$ .

STEP 7

The difference between the model's prediction and the actual number is given by $Difference = -_{actual}$ If the difference is positive, the model overestimates the actual number. If the difference is negative, the model underestimates the actual number.

STEP 8

Without the actual graph, we cannot calculate the exact difference. However, we can compare the difference with the options given in the problem. The options suggest that the difference is either0.2 or0.4.

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QuestionFind the foreign-born percentage, P, in 1990 using $P=0.0021 x^{2}-0.286 x+16.28$ . Does it overestimate or underestimate?

Studdy Solution

STEP 1

STEP 2

First, we need to find the value of $x$ for the year1990. Since $x$ represents the years after1900, we can calculate $x$ as follows $x =1990 -1900$

STEP 3

Calculate the value of $x$ .
$x =1990 -1900 =90$

STEP 4

Now, we can substitute $x =90$ into the model to find the percentage of the U.S. population that was foreign-born in1990.
$=0.0021 \times90^{2} -0.286 \times90 +16.28$

STEP 5

Calculate the value of $$.
$=0.0021 \times90^{2} -0.286 \times90 +16.28 =8.9$ So, according to the model,8.9% of the U.S. population was foreign-born in1990.

STEP 6

Next, we need to compare the model's prediction with the actual number displayed on the graph. Since the actual problem does not provide the graph, we will assume that the actual number displayed on the graph is $_{actual}$ .

STEP 7

The difference between the model's prediction and the actual number is given by $Difference = -_{actual}$ If the difference is positive, the model overestimates the actual number. If the difference is negative, the model underestimates the actual number.

STEP 8

Without the actual graph, we cannot calculate the exact difference. However, we can compare the difference with the options given in the problem. The options suggest that the difference is either0.2 or0.4.

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QuestionFind the foreign-born percentage, P, in 1990 using P=0.0021x2−0.286x+16.28P=0.0021 x^{2}-0.286 x+16.28P=0.0021x2−0.286x+16.28. Does it overestimate or underestimate?

Studdy Solution

STEP 1

STEP 2

First, we need to find the value of xxx for the year1990. Since xxx represents the years after1900, we can calculate xxx as followsx=1990−1900x =1990 -1900x=1990−1900

STEP 3

Calculate the value of xxx.x=1990−1900=90x =1990 -1900 =90x=1990−1900=90

STEP 4

Now, we can substitute x=90x =90x=90 into the model to find the percentage of the U.S. population that was foreign-born in1990.=0.0021×902−0.286×90+16.28 =0.0021 \times90^{2} -0.286 \times90 +16.28=0.0021×902−0.286×90+16.28

STEP 5

Calculate the value of $$.=0.0021×902−0.286×90+16.28=8.9 =0.0021 \times90^{2} -0.286 \times90 +16.28 =8.9=0.0021×902−0.286×90+16.28=8.9So, according to the model,8.9% of the U.S. population was foreign-born in1990.

STEP 6

Next, we need to compare the model's prediction with the actual number displayed on the graph. Since the actual problem does not provide the graph, we will assume that the actual number displayed on the graph is actual_{actual}actual​.

STEP 7

The difference between the model's prediction and the actual number is given byDifference=−actualDifference = -_{actual}Difference=−actual​If the difference is positive, the model overestimates the actual number. If the difference is negative, the model underestimates the actual number.

STEP 8

Without the actual graph, we cannot calculate the exact difference. However, we can compare the difference with the options given in the problem. The options suggest that the difference is either0.2 or0.4.

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the foreign-born percentage, P, in 1990 using $P=0.0021 x^{2}-0.286 x+16.28$ . Does it overestimate or underestimate?

First, we need to find the value of $x$ for the year1990. Since $x$ represents the years after1900, we can calculate $x$ as follows $x =1990 -1900$

Calculate the value of $x$ .
$x =1990 -1900 =90$

Now, we can substitute $x =90$ into the model to find the percentage of the U.S. population that was foreign-born in1990.
$=0.0021 \times90^{2} -0.286 \times90 +16.28$

Calculate the value of $$.
$=0.0021 \times90^{2} -0.286 \times90 +16.28 =8.9$ So, according to the model,8.9% of the U.S. population was foreign-born in1990.

Next, we need to compare the model's prediction with the actual number displayed on the graph. Since the actual problem does not provide the graph, we will assume that the actual number displayed on the graph is $_{actual}$ .

The difference between the model's prediction and the actual number is given by $Difference = -_{actual}$ If the difference is positive, the model overestimates the actual number. If the difference is negative, the model underestimates the actual number.