Problema Solution
year 1940 1968 1997
wage ($) 0.25 1.60 5.15
Minimum Wage The table shows the minimum wage for
three different years.
(a) Make a scatterplot of the data in the viewing rectangle
[1930, 2010, 10] by [0, 6, 1].
(b) Find a quadratic function given by f(x)=a(x-h)squared + k
that models the data.
(c) Estimate the minimum wage in 1976 and compare
it to the actual value of $2.30.
(d) Estimate when the minimum wage was $1.00.
(e) If current trends continue, predict the minimum
wage in 2009. Compare it to the projected value of
$7.25.
Answer provided by our tutors
(b) Equation: y=0.00130174574x^2-5.03900808x+4876.675395 with a R^2 value of 1, meaning that this is a perfect fit.
To write this in the y=A(x-h)^2+k form, find the vertex of the parabola: (1935.4809,.2234)
So you get for part b) f(x)=0.0013(x-1935.4809)^2+0.22341555
(c) If you want to know the minimum wage at any year, simply plug that year into your equation and calculate f(year).
So f(1976)=2.361 and differs from the actual value by 0.061.
(d) To find when the minimum wage was $1, plug 1 in for y and solve for x.
In this case, you get x=1911.056 or x=1959.906
(e) To find the predicted minimum wage of 2009, plug in for x in the equation.
f(2009)=7.259, which differs from the projected value by 0.009.