The total amount spent by some number of people on clothing and footwe

podnescijy

podnescijy

Answered question

2021-11-30

The total amount spent by some number of people on clothing and footwear in the years 2000-2009 can be modeled by the quadratic function f(x)=4.509x2+71.12x+97.91, where x=0 represents January 1, 2000, x=1 represents January 1, 2001, and so on, and f(x) is in billions of dollars. According to the model, in what year during this period was the amount spent on clothing and footwear a maximum?

Answer & Explanation

Rex Gibbons

Rex Gibbons

Beginner2021-12-01Added 6 answers

 f(x)=4.509x2+71.12x+97.91
f(x)=d dx (4.509x2+71.12x+97.91)
=d dx (4.509x2)+d dx (71.12x)+d dx (97.91)
=9.018x+71.12+0
f(x)=9.018x+71.12
Let f(x)=0
9.018x+71.12=0
9018x=71120
x=7.886
d2 dx 2(f(x))=d dx (9.018x+71.12)
=d dx (9.018x)+d dx (71.12)
=9.018<0
So, at x=7.886, f(x) maximum
f(x) at x=7.886
f(7.886)=4.509×7.8862+71.12(7.886)+97.91=378.35
AndPSKx=7.8868

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