SOLUTION: I need your help please. 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 + 3

This problem is botched, either by you, your
teacher or your textbook author.

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)

You left off the n.  So I will assume the formula was supposed to
be

   s = 0.038n + 21.2

a.  How many senior citizens were there in 2000?

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 

The percentage of senior citizens living below [poverty] 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%.

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.


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.

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