The population (in millions) of the United States between 1970 and 2010 can be modeled asp(x) 203.12e0.011x million peoplewhere x is the number of decades after 1970.The percentage of people in the United States who live in the Midwest between 1970 and 2010 can be modeled asm(x) = 0.002x2 - 0.213x 27.84 percentwhere x is the number of decades since 1970.tHow rapidly was the population of the Midwest changing in 2000 and in 2010? (Round your answers to three decimal places.)x million people per decade0.20620000.2132010million people per decade

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Asked Nov 4, 2019
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The population (in millions) of the United States between 1970 and 2010 can be modeled as
p(x) 203.12e0.011x million people
where x is the number of decades after 1970.
The percentage of people in the United States who live in the Midwest between 1970 and 2010 can be modeled as
m(x) = 0.002x2 - 0.213x 27.84 percent
where x is the number of decades since 1970.t
How rapidly was the population of the Midwest changing in 2000 and in 2010? (Round your answers to three decimal places.)
x million people per decade
0.206
2000
0.213
2010
million people per decade
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The population (in millions) of the United States between 1970 and 2010 can be modeled as p(x) 203.12e0.011x million people where x is the number of decades after 1970. The percentage of people in the United States who live in the Midwest between 1970 and 2010 can be modeled as m(x) = 0.002x2 - 0.213x 27.84 percent where x is the number of decades since 1970.t How rapidly was the population of the Midwest changing in 2000 and in 2010? (Round your answers to three decimal places.) x million people per decade 0.206 2000 0.213 2010 million people per decade

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Step 1

Given:

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The population ofUS between 1970 and 2010 is given as p(x) = 203.12e 'wherex is the number of decades since 1970. The percentage of people in US who live in Midwest between 1970 and 2010 is given as m(x) 0.002x2-0.213x+27.84 % wherex is the number of decades since 1970. Suppose the population ofpeople in US who live in Midwest be M(x), then м (х). x100 m(x)=

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Step 2

Thus, the population of people in US who live in Midwest becomes

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т(x) p(х) M(x) 100 (0.002x2 -0.213x +27.84)203.12e0011 100 In order to obtain the change in population ofMidwest in 2000 and 2010, differentiate M(x)with respect to x (0.004x -0.213) (0.002x-0.213x +27.84)2.23432e м («)-. 0.011x 0.011x 203.12e 100

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Step 3

Do:

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Substitutex-3 for 2000 in the equation of M'(x) and obtain the change in population of Midwest in 2000. 0.011(3) (0.002(3)-0.213 (3)+27.84)2.23432e° м'(3)- +203.12e (0.004(3)-0.213) 100 (0.018-0.639+27.84)2.23432e0 203.120(0.012-0.213) 0.033 100 0.20659. 0.207

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Math

Calculus