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) = 0.002x^2 0.213x + 27.84 percent where x is the number of decades since 1970.

(a) Write an expression for the number of people who live in the Midwest x decades after 1970.

(b) Write an expression for the rate of change of the population of the Midwest.

(c) How rapidly was the population of the Midwest changing in 1990 and in 2000? (Round your answers to three decimal places.)

Explanation / Answer

a)number of people who live in midwest x decades after 1970 are

(0.002x^2 -0.213x +27.84)(203.12e^(0.011x))/100

P=(0.40624x^2e^(0.011x) -43.264xe^(0.011x) +5654.8608e^(0.011x))/100

b) dP/dx =0.33658xe^(0.011x) +18.93947e^(0.011x) +0.00447x^2 e^(0.011x)

c) at x =20 means 1990

dP/dx = 0.33658 *20*e^(0.22) +18.93947e^(0.22) +0.00447*400*e^(0.22)

=8.3875 +23.598 +2.2278

=34.2133

for x=30 means 2000

= 0.33658 30*e^(0.33) +18.93947e^(0.33) +0.00447*900*e^(0.33)

=14.0444 +26.3429 +5.5955

=45.9828

Thank you

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