a) The function that models the cost per share with respect to the number of new contributors can be calculated as follows:
Let x be the total number of contributors (including the initial seven contributors) and y be the cost per share. If the total cost of the table is $900 and there are x contributors, then the cost per share, y, can be calculated as:
y = Total cost / Total contributors
y = $900 / x
Since Erin already has seven contributors signed up, the number of new contributors is p, so the total number of contributors is x = 7 + p. Therefore, the function that models the cost per share with respect to the number of new contributors is:
C(p) = $900 / (7 + p)
b) To find out how many new contributors Erin must recruit in order for the cost of each share to be $50, we can set the cost per share (C) to $50 and solve for p:
$50 = $900 / (7 + p)
$50 * (7 + p) = $900
350 + 50p = $900
50p = $550
p = 11
Therefore, Erin must recruit 11 new contributors in order for the cost of each share to be $50.