(a) To find the minimum wage in 1995, we substitute x=1995-1970=25 into the equation:
y = 0.15x^2.92
y = 0.15(25)^2.92
y ≈ 0.15(656.1)
y ≈ 98.415
The minimum wage in 1995 was approximately $98.42.
(b) To estimate the minimum wage in 2005, we substitute x=2005-1970=35 into the equation:
y = 0.15x^2.92
y = 0.15(35)^2.92
y ≈ 0.15(2252.4854)
y ≈ 337.873
The minimum wage in 2005 was approximately $337.87.
(c) The y-intercept is the value of y when x=0. Substituting x=0 into the equation:
y = 0.15x^2.92
y = 0.15(0)^2.92
y = 0
The y-intercept is 0. In the context of this problem, it means that in the year 1970, the minimum wage was approximately $0 per hour. This could be because there was no federal minimum wage in place at that time.
(d) The slope represents the rate at which the minimum wage is changing over time. In this case, the slope is 0.15. This indicates that the minimum wage has increased by approximately $0.15 per year during this period.
The minimum hourly wage,
y
(in dollars per hour), in a country can be approximated by the equation
=y+0.15x2.92
. In this equation,
x
represents the number of years since
1970
=x=0 represents 1970, x5 represents 1975, and so on
.
Federal Minimum Hourly Wage by Year
(a) Use the equation to approximate the minimum wage in the year
1995
.
The minimum wage in
1995
was approximately
$
.
(b) Use the equation to estimate the minimum wage in the year
2005
.
The minimum wage in
2005
was approximately
$
.
(c) Determine the
y
-intercept. Interpret the meaning of the
y
-intercept in the context of this problem.
The
y
-intercept is
,
. In the year
the minimum wage was approximately
$
per hour.
(d) Determine the slope. Interpret the meaning of the slope in the context of this problem.
The slope is
. This indicates that the minimum wage has (increased or decreased) by approximately
$
per year during this period.
1 answer