The function px11x240x1040 models the amount px in billions

The function ?p(x)=11x²+40x+1040 models the? amount, p(x), in billions of? dollars, that a government spent on human resources x years after 1970. The function q(x)=12x²+230x+2190 models total budget? expenditures, q(x), in billions of? dollars, x years after 1970.

?(a) Use p and q to write a rational function that models the fraction of total budget outlays spent on human resources x years after 1970.

?f(x)= [ ] ?

(b) Use the data displayed by the bar graph to find the percentage of federal expenditures spent on human resources in 2006 .

     [ ] ?% ?(Round to the nearest percent as? needed.) ?

(c) Use the rational function from part ?(a) to find the percentage of federal expenditures spent on human resources in 2006 .

      [ ]?% ?(Round to the nearest percent as? needed.)

Does the preceding result underestimate or overestimate the actual percent found in part ?(b).

      [ ] Overestimates

      [ ] Underestimates

By how much does the calculated percent overestimate the actual? percent?

    [ ] ?%

?(d) What is the equation of the horizontal asymptote associated with the rational function in part ?(a)?? Select the correct choice below and fill in any answer boxes within your choice.

       [ ] A. yequals nothing ?(Type an integer or a simplified? fraction.)

       [ ] B. There is no horizontal asymptote.

If trends modeled by the function? continue, what percentage of the federal budget will be spent on human resources over? time?

   [ ] ?% ?(Round to the nearest percent as? needed.)

Solution

a) (fraction of total budget outlays spent on human resources x years after 1970)

.f(x) = p(x)/q(x) = (11x^2+40x+1040)/(12x^2+230x+2190)

b) From 2006 :percentage of federal expenditures spent on human resources in 2006 = (1700/2800)*100 = 60.7% = 61%

c) x = 36 .Plug x= 36 in f(x) = (11*36^2 + 40*36 +1040)/( 12*36^2 +230*36 +2190)

= 16736/ 26022 = 0.643 = 64.3% = 64%

Result overestimates the result in part b

d) It oversetimates by =64.3 -60.7 = 3.6 % = 4%

e) If trends continue

.f(x) = p(x)/q(x) = (11x^2+40x+1040)/(12x^2+230x+2190)

for x>>>

f(x) = 11x^2/12x^2 = 11/12 = 0.916 = 91.67 % = 92%