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.

Explanation:

Step1: Substitute x=30 into G(x)

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

Step2: Calculate squared term

$(30)^2 = 900$, so $-0.01 \times 900 = -9$

Step3: Sum remaining terms

$-9 + 30 + 55 = 76$

Step4: Interpret the result

x=30 means 30 years after 1980, which is 2010. G(x) is a percent.

Answer:

C. G(30)=76, which represents a wage gap of 76% in the year 2010.