Expert: Richard J. Raridon - 3/14/2004

Question
For 1990 through 1992, the number of banks in the US can be modeled by
K = 1,228,230 + 36,590t^2
   ---------------------
    100 + 4.66t^2
where K is the number of banks and t is the year, t=0 corresponding to 1990.

For 1990 through 1992, the number of branches in the US can be modeled by
R = 505,430 + 9661t^2
   ------------------
      10 + 0.128t^2
where R is the number of branches and t is the year, with t=0 corresponding to 1990.

1. Find the total number of commercial banks in the US in 1992.

2. In what year did the total number of commercial banks grow to more than 66,000?

3. To find the average number of branches per bank, divide the number of branches by the number of banks. Write an equation that represents the average number of branches per bank. Simplify the result.

4. Find the average number of branches per bank in 1996.

I am completely lost on this one.  Please help.  Need for class tomorrow.  Hope you get this in time.  

Answer
First of all, you don't want to use commas in an algebraic expression.  
I assume you have K = (1228230+36590t^2)/(100+4.66t^2)
Is that correct?
1. If you put in t=2, K = 11553 banks
2. This expression decreases with increasing t so that you can't get to 66,000.