SOLUTION: The percentage of companies with at least one woman on the Board is growing steadily (Forbes, February 10, 1997). The percentage of companies can be approximated with the linear e

The percentage of companies with at least one woman on the Board is growing
steadily (Forbes, February 10, 1997). The percentage of companies can be
approximated with the linear equation

p = 2n + 36

where n is the number of years since 1980.

a) Find and explain the meaning of the p-intercept for the line. 
b) Find and explain the meaning of the n-intercept for the line. 


An intercept is the value of THAT quantity when the OTHER quantity is 0.

The p-intercept is the value of p when the other letter n is 0.
The n-intercept is the value of n when the other letter p is 0.

To find the p-intercept, substitute 0 for n, and solve for p

p = 2n + 36
p = 2(0) + 36
p = 36

So 36 is the percentage of companies with at least one woman on board, when
n = 0, that is, when 0 years have past, which means "at the beginning", i.e.,
in 1980.

To state that better:  In 1980, 36% of the companies had at least one woman 
on board. 

To find the n-intercept, substitute 0 for p, and solve for n

p = 2n + 36
0 = 2n + 36
-36 = 2n
  n = -18

This being a negative number, it means that 18 years BEFORE 1980 was when
0% of the companies had at least one woman on board.

To state that better:  In 1962, none of the companies had any women on board.
 
--------------------------------

c) If this trend continues, then in what year would you expect to find nearly
all companies having at least one woman on the Board? 

This would be when the percentage p is 100%.  So we substitute 100 for p and
solve for n:

  p = 2n + 36
100 = 2n + 36
 64 = 2n
 32 = n

So 32 years after 1980 is when 100% of the companies will have at least one
woman on board.

To say that better:  In 2012 all the companies will have women on board.

Edwin