Word problem

Question

Hiv/Aids Federal funding f in billions of dollars for hiv/aids research from 1981 to 2006 can be modeled by f=0.0316x^2+0.015x-0.046. Where x=1 corresponds to 1981, x=2 corresponds to 1982, and so on until x=2 corresponds to 2006

a. estimate federal funding for Hiv/Aids research in 2001

b Use a table of values to estimate the year in which federal funding for Hiv/Aids research reached $18.5billion.ails as possible.

Answer 1

a.) for 2001, x = 21

Substitue x = 21 into the equation :

f(21) = .0316 (21)² + .015 (21) - 0.046 = 14.2046

Answer: 14.2046 Billion dollars

 

b.) You can enter an equation into (almost) any graphing calculator and it has an option to view both the graph and the table. 

when x = 24, f(x) = 18.516

x = 24 corresponds to 2004.

Answer: 2004

Answer 2

Given:     ƒ(x) = 0.0316x² + 0.015x - 0.046 

         x = time (in years) from 1981 to 2006 , 

where   1981:   x = 1 ,   1982:   x = 2 , ... ,   2006: x = 26

(a) the year 2001 corresponds to  x = 21

     to determine federal funding for research in 2001, compute ƒ(21)

     ƒ(21) = 0.0316(21)² + 0.015(21) - 0.046

              = 14.2046

              ≈ 14.2 

   thus, federal funding for research in 2001 was approximately $14.2 billion 

(b) when determining the year in which funding for research reached $18.5 billion, since we know in 2001 it reached $14.2 billion then it must have reached 18.5 billion in one of the following 5 years. if we first compute the funding for the last year (2006) which is the 26th year (i.e., x = 26) we can determine where 18.5 will fall in the years in between.

     ƒ(26) = 0.0316(26)² + 0.015(26) - 0.046

              = 21.7056

              ≈ 21.7

therefore, since funding in 2001 (x = 21) was 14.2 billion and in year 2006 (x = 26) was 21.7 billion, then 18.5 billion should fall somewhere in the middle. that is, funding should have reached 18.5 billion either in the 23rd or 24th year. so we compute ƒ(23) to see if it's under or over 18.5:

     ƒ(23) = 0.0316(23)² + 0.015(23) - 0.046

             = 17.0154 ≈ 17.0 

with this, funding must have reached 18.5 in one of following years. compute ƒ(24):

     ƒ(24) = 0.0316(24)² + 0.015(24) - 0.046 

              = 18.5156 ≈ 18.5

thus, federal funding for research reached $18.5 billion in the 24th year which corresponds to 2004.