Question

the bar graph shows the wage gap between men and women for selected years from 1980 through 2020. the function ( g(x) = -0.01x^2 + x + 55 ) models the wage gap, as a percent, ( x ) years after 1980. the graph of function ( g ) is also shown. use this information to complete parts a and b.
a. find and interpret ( g(30) ).
a. ( g(30) = 81 ), which represents a wage gap of 81% in the year 2010.
b. ( g(30) = 76 ), which represents a wage gap of $76,000 in the year 2010.
c. ( g(30) = 76 ), which represents a wage gap of 76% in the year 2010.
d. ( g(30) = 81 ), which represents a wage gap of $81,000 in the year 2010.
identify this information as a point on the graph of the function.
this information is represented by the point \\( \square \\). (type an ordered pair.)

Explanation:

Step1: Substitute x=30 into G(x)

$G(30) = -0.01(30)^2 + 30 + 55$

Step2: Calculate squared term

$-0.01(900) + 30 + 55$

Step3: Compute multiplication

$-9 + 30 + 55$

Step4: Sum the values

$76$

Step5: Define ordered pair

x=30 (years after 1980), G(30)=76, so the pair is (30, 76)

Answer:

A. (Multiple Choice) C. G(30)=76, which represents a wage gap of 76% in the year 2010.
B. (Ordered Pair) (30, 76)