Solve the problem.
-The formula models the percentage of female tenured faculty, F, at State University x years after 1980. According to the formula, in what year will the percentage of female tenured faculty reach 31.52?
A) 2005
B) 2007
C) 2006
D) 2008

Question

Solve the problem.
-The formula  models the percentage of female tenured faculty, F, at State University x years after 1980. According to the formula, in what year will the percentage of female tenured faculty reach 31.52?
A) 2005 
B) 2007 
C) 2006 
D) 2008

Quizplus · Accepted Answer

Since the formula represents the percentage of female tenured faculty x years after 1980, we need to solve the equation 11ebb63d_1be3_17f3_b851_2d3bf7220a58_TB8475_11 = 31.52 for x.

Setting the equation equal to 31.52, we get:

31.52 = 11ebb63d_1be3_17f3_b851_2d3bf7220a58_TB8475_11

To solve for x, we need to isolate it on one side of the equation. First, we can simplify the expression on the right side of the equation:

11ebb63d_1be3_17f3_b851_2d3bf7220a58_TB8475_11 = (1 - 0.003)^x * 100

11ebb63d_1be3_17f3_b851_2d3bf7220a58_TB8475_11 = 0.997^x * 100

Taking the natural logarithm of both sides of the equation, we get:

ln(31.52) = ln(0.997^x * 100)

ln(31.52) = ln(0.997^x) + ln(100)

ln(31.52) = x*ln(0.997) + ln(100)

To solve for x, we can divide both sides by ln(0.997):

x = (ln(31.52) - ln(100)) / ln(0.997)

Using a calculator, we find that x is approximately equal to 25.99.

Since x represents the number of years after 1980, we can add 1980 to get the year when the percentage of female tenured faculty will reach 31.52:

1980 + 25.99 ≈ 2006

Therefore, the answer is C) 2006. Since the formula is in terms of years after 1980, we can set up the equation:
11ebb63d_1be3_17f3_b851_2d3bf7220a58_TB8475_11 = 31.52
Solving for x, we get x = 26. Plugging this into the formula, we get 1980 + 26 = 2006. Therefore, the percentage of female tenured faculty will reach 31.52 in the year 2006.

Solve the Problem. -The Formula Models the Percentage of Female Tenured Faculty