Imports (in billions of dollars) from country A to country B have changed at the

Question

Imports (in billions of dollars) from country A to country B have changed at the rate of g(x) = 0.12x2 + 0.32x + 11.52, where x is the number of year since 2000. Country A important $220.72 billion worth of goods in 2001. Find a function giving the value of imports x years after 2000. What was the value of imports from country A in 2005? What is the function for the value of imports? G(x) = (Simplify your answer. Use integers or decimals for any numbers in the expression.) The value of imports from country A in 2005 was $ billion. (Type an integer or a decimal.)

Explanation / Answer

g(x)=0.12x2+0.32x+11.52

a)G(x)=integral(0.12x2+0.32x+11.52) dx

G(x)=(0.12x3/3 +0.32x2/2+11.52x)+c

G(x)=(0.04x3 +0.16x2+11.52x)+c

in 2001==>x=2001-2000=1

G(x)=(0.04*13 +0.16*12+11.52)+c=220.72

==>11.72+c=220.72

==>c=209

G(x)=0.04*x3 +0.16*x2+11.52x+209

b)in 2005==>x=2005-2000=5

G(5)=0.04*53 +0.16*52 +11.52*5 +209

G(5)=275.6 billion $

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