Question

1. The table shows the minimum wage rates for the United States during different years.

Year 1978 1979 1980 1990 1991 1996 1997 2007 2008 2009
Minimum hourly wage ($) 2.65 2.90 3.35 3.80 4.25 4.75 5.15 5.85 6.55 7.25

(a) On the line below, write the least squares regression equation that models the data. Let x = time in years since 1900 and let y = minimum hourly wage. Use Desmos, and do not round the equation it gives you.
____________________________________________________________________________
(b) Use the equation to estimate the minimum hourly wage of a U.S. worker in 2025. Use Desmos and round to the nearest cent.
Minimum hourly wage = ________________________________________________________
Include “Snips” or screenshots showing everything you typed into Desmos.



2The table shows the soil density of several soil samples at different depths.

Depth (m) 1 5 6 8 10 12 14 21 23 24 28
Soil density ( )
1045 1063 1102 1140 1191 1232 1249 1254 1265 1268 1273

(a) On the line below, write the quadratic regression equation that models the data. Let x = depth below the surface and let y = soil density. Use Desmos, and do not round the equation it gives you.
________________________________________________________________________
(b) Use the equation to estimate the soil density of a sample at a depth of 20 m. Use Desmos, and round the density to the nearest whole number.
Soil density = __________________________________________________________
¬¬¬¬¬¬
Include “Snips” or screenshots showing everything you typed into Desmos

Answer 1

A) Y = 0.4931x2 + 23.3798 + 996.0289

B) X = 20

Explanation:

Answer 2

1.

(A) y = 0.126X - 7.119

(B) 8.63

X = year, we subtract the year in the data from 1900;

So, for the years we have:

78,79,80,90,91,96,97,107,108,109

Using technology to fit the data above, the regression model obtained is;

y = 0.126X - 7.119

Where x = years

y = minimum hourly wage

The minimum hourly wage in 2025

Year = x = 2025 - 1900 = 125 years

y = 0.126(125) - 7.119

y = 8.631 Predicted Minimum hourly wage = 8.63

2.

(A) y = -0.4931x^2 + 23.3798x + 996.0289

(B) x = 20

y = -0.4931x^2 + 23.3798x + 996.0289

y = -0.4931(20)^2 + 23.3798(20) + 996.0289

y = -0.4931(400) + 467.596 + 996.0289

y = -197.24 + 467.596 + 996.0289

y = 1266.3849