Question 39079
<PRE><font size = 4><b><i><font color = "indigo">This problem is botched, either by you, your
teacher or your textbook author.</i></font>

The number of senior citizens (65 and over) in the United States in 
millions n years after 1990 can be estimated by using the formula.
   s = 0.038 + 31.2  US Bureau of the Census)

<i><font color = "indigo">You left off the n.  So I will assume the formula was supposed to
be

   s = 0.038n + 21.2</i></font>

a.  How many senior citizens were there in 2000?

<font color = "indigo"><i>2000 is 10 years after 1990, so plug 10 in the formula

   s = 0.038n + 31.2
   s = 0.038(10) + 31.2
   s = 31.58 million</i></font> 

The percentage of senior citizens living below <i><font color = "indigo">[poverty]</i></font> level 
n years after 1990 can be estimated by using the formula.

   p = 0.25n + 12.2

b.  In what year will the percentage of seniors living below the 
poverty level reach 7%.

<font color = "indigo"><i>There is something wrong here because according to that formula in
1990, 0 years after 1990, the percentage was 12.2%. And, in 1991, the
percentage was 12.45% and the percentage keeps going up after that.
Thus is had already reached 12.2% in 1990.  So it must have reached
7% long before 1990!  Be sure to ask your teacher if this problem was
not in error.  But let's solve it anyway and see what happens:

Plug 7 in for p and solve for n

           p = 0.25n + 12.2
           7 = 0.25n + 12.2

 Clear of decimals by multiplying through by 100

         700 = 25n + 1220

  700 - 1220 = 25n
        -520 = 25n
     -520/25 = n
       -20.8 = n

or approximately -21 years AFTER 1990, which means
21 years BEFORE 1990 or way back in 1969.  

So it reached 7% way back in 1969 and it didn't
reach 12.2% until 21 years later in 1990.

But surely this is not what you were given.  Be sure
to ask your teacher.</i></font>


c.  What is the first year in which can we expect both 
the number of seniors to be greater than 49 million and 
fewer than 7% living below the poverty level.

<font color = "indigo"><i>This is impossible, because it hasn't been below 7% since
before 1969, and back then, using the formula that you left
off the n in, and I guessed it was supposed to be after the
0.038, substituting -21 for n (21 years before 1990),

   s = 0.038n + 31.2
   s = 0.038(-21) + 31.2
   s = 30.402 million

So back when the poverty level was below 7% there were
fewer than 49 million -- in fact, less than 31 million.

Please check the assignment carefully and/or ask your
teacher.

Edwin McCravy
AnlytcPhil@aol.com</i></PRE></font>