The table shows the minimum wage for three different years.
Year 1940, 1968,1997
wages for 1940 $.025, 1968 $1.60, 1997 $5.15
estimate the minimum wage in 1976 and compare it to the actual value of $2.30
and estimate when the minimum wages was $1.00.
If the current trends continue, predict the minimum wage in 2009. Compare it to the projected value of $7.25
Make a scatterplot of the data in the viewing rectangle (1930,2010, 10) by (0,6,1)
To estimate the minimum wage in a given year, you can analyze the trend by looking at the change in minimum wage over time.
1. Estimating the minimum wage in 1976:
To estimate the minimum wage in 1976, we can look at the trend between 1968 and 1997. In this period, the minimum wage increased from $1.60 in 1968 to $5.15 in 1997. We can calculate the average yearly increase during this period and apply it to 1976.
Average yearly increase:
(1997 minimum wage - 1968 minimum wage) / (1997 year - 1968 year)
= ($5.15 - $1.60) / (1997 - 1968)
= $3.55 / 29
≈ $0.1224
Minimum wage in 1976 estimation:
Minimum wage in 1976 = (1968 minimum wage) + (difference in years) × (average increase per year)
= $1.60 + (1976 - 1968) × $0.1224
= $1.60 + 8 × $0.1224
≈ $1.97
Comparing with the actual value of $2.30, the estimated minimum wage in 1976 ($1.97) is slightly lower.
2. Estimating when the minimum wage was $1.00:
To estimate the year when the minimum wage was $1.00, we can use the 1968 minimum wage as a reference. We can calculate the difference between $1.00 and $1.60 to determine the decrease per year.
Decrease per year:
$1.60 - $1.00 = $0.60
Number of years to reach $1.00:
Number of years = (Difference in minimum wage) / (Decrease per year)
= $0.60 / $0.60
= 1 year
Therefore, the minimum wage was estimated to be $1.00 in 1969.
3. Predicting the minimum wage in 2009:
To predict the minimum wage in 2009, we can continue the trend using the same average yearly increase we calculated earlier.
Minimum wage in 2009 prediction:
Minimum wage in 2009 = (1997 minimum wage) + (difference in years) × (average increase per year)
= $5.15 + (2009 - 1997) × $0.1224
= $5.15 + 12 × $0.1224
≈ $6.82
Comparing with the projected value of $7.25, the predicted minimum wage in 2009 ($6.82) is slightly lower.
4. Scatterplot of the data:
To create a scatterplot of the data, we will use the viewing rectangle (1930, 2010, 10) by (0, 6, 1).
On the x-axis, we will represent the years, and on the y-axis, we will represent the minimum wage. Each data point (year, minimum wage) will be plotted on the graph.
Note: Unfortunately, as a text-based AI, I cannot generate visual content like graphs. However, you can draw a scatterplot using the provided information and axis ranges on a piece of paper or using any graphing software.