The population (in millions) of the United States between 1970 and 2010 can be m

Question

The population (in millions) of the United States between 1970 and 2010 can be modeled as

p(x) = 203.12e^0.011x 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.† How rapidly was the population of the Midwest changing in 1990 and in 2010? (Round your answers to three decimal places.)

1990 million people per decade 2010 million people per decade

Explanation / Answer

Total population living in midwest in united states is p(x)m(x)/100

=(2031.12e^0.11x)(0.002x^2 -0.213x +27.84)/100

P=(4.062x^2e^0.11x - 0.432x e^0.11x +56546.38)/100

dP/dx =1/100(0.44682x^2e^0.11x +8.076xe^0.11x -0.432e^0.11x)

dP/dx in 1990 means x =20

=(0.44682*400*e^2.2 +8.076*20*e^2.2 -0.432e^2.2)/100

=(1612.12 +1456.91-3.896)/100

=30.65

in 2010 means x =40

=(0.44682*1600*e^4.4 +8.076*40*e^4.4 -0.432e^4.4)/100

=(58229.5824 +26311.608 -35.1864)/100

=845.06 million people per decade

Thank you

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.