The table shows the closing value of a stock index for one week in March, 2004.
a. Using the day as the x-value and the closing value as the y-value, write equations in slope-intercept form for the lines that represent each value change.
b. What would indicate that the rate of change for two pair of days was the same? Was the rate of change the same for any of the days shown?
c. Use each equation to predict the closing value for the next business day (Day 22). The actual closing value was 1909.90. Did any equation correctly predict this value? Explain.
Stock Index
March, 2004
____________________________
Day Closing Value
15 - 1939.20
16 - 1943.09
17 - 1976.76
18 - 1962.44
19 - 1940.47
Calculate Dy/Dx if y = LN (2x3 + 3x)
a. To write equations in slope-intercept form for the lines that represent each value change, we need to calculate the slope and y-intercept for each line.
Let's name the x-values as "Day" and the y-values as "Closing Value." The table is not provided, so I cannot give you the actual values. However, I can explain the process.
For each pair of points, (x1, y1) and (x2, y2), the slope can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
The slope-intercept form of a linear equation is:
y = mx + b
where m is the slope and b is the y-intercept.
For each pair of consecutive points, you can find the slope and y-intercept to write the equation.
b. The rate of change for two pair of days would be the same if the slopes of their respective lines are equal. If the slopes are different, the rate of change would be different.
To determine if the rate of change is the same for any of the days shown, you need to compare the slopes of the lines. If there are pairs of lines with equal slopes, then the rate of change is the same for those days.
c. To predict the closing value for the next business day (Day 22), you need to use each equation and substitute 22 for x in each equation. This will give you the predicted closing value for Day 22.
Compare the predicted values obtained from each equation with the actual closing value of 1909.90. If any equation gives a predicted value equal to 1909.90, that equation correctly predicts the closing value. Otherwise, none of the equations correctly predict the value.
Please note that without the actual values or equations, I cannot provide specific calculations or answers. However, I hope this explanation helps you understand the process of finding the equations, comparing slopes, and predicting values.