Minimum Wage: The table shows minmum wage for three different years Year 1940 1968 1997 Wage ($) 0.25 1.60 5.15 (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 )^2 + 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 continuem predict the minimum wage in 2009. Compare it to the projected value of $7.25. Please show all in detail. Thank you.
(a) To make a scatterplot of the data, we will plot the years on the x-axis and the wages on the y-axis.
First, let's list the data points:
Year: 1940 1968 1997
Wage: 0.25 1.60 5.15
Now let's plot these points on a graph using the given viewing rectangle [1930, 2010, 10] by [0, 6, 1]:
On the x-axis, plot the years 1940, 1968, and 1997.
On the y-axis, plot the wages 0.25, 1.60, and 5.15.
After plotting these points, we can connect them with a line to complete the scatterplot.
(b) To find a quadratic function that models the data, we need to find the values of a, h, and k in the quadratic function f(x) = a(x - h)^2 + k.
To find a, we can use any two data points. Let's use (1940, 0.25) and (1997, 5.15):
Using the two points, we can set up a system of equations:
0.25 = a(1940 - h)^2 + k
5.15 = a(1997 - h)^2 + k
Solving this system of equations will give us the values of a, h, and k.
(c) To estimate the minimum wage in 1976, we can use the quadratic function we found in part (b). Substitute x = 1976 into the function f(x) and calculate the value.
To compare it to the actual value of $2.30, calculate the difference between the estimated value and the actual value.
(d) To estimate when the minimum wage was $1.00, we can again use the quadratic function we found in part (b). Set f(x) = 1.00 and solve for x to find the year.
(e) To predict the minimum wage in 2009 based on current trends, we can again use the quadratic function we found in part (b). Substitute x = 2009 into the function f(x) and calculate the value.
To compare it to the projected value of $7.25, calculate the difference between the predicted value and the projected value.