the table below shows the attendance in millions at theme parks in a certain country. Make a scatter plot of the data pairs. Draw a trend line and write its equation. Estimate the attendance at theme parks in the country in 2005.
Year 1990 1992 1994 1996 1998 2000 2002 2004 2006
Attendance (millions) 250 266 268 292 300 319 322 329 339
Let x be the year and let y be the attendance that year in millions. Make a scatter plot of the data pairs and draw a trend line. Choose the correct graph below. Substitute 2005 for x in the equation for the trend line and simplify
To make a scatter plot of the data pairs, we plot the years (x-values) on the x-axis and the attendance (y-values) on the y-axis.
Here's the scatter plot:
Year (x) Attendance (y)
1990 250
1992 266
1994 268
1996 292
1998 300
2000 319
2002 322
2004 329
2006 339
Now, we can draw a trend line that represents the general pattern of the data points.
After plotting the points, we can see that there is a general upward trend in attendance over time. Let's draw a trend line that approximately fits the points.
The equation of a trend line is typically written in the form y = mx + b, where m represents the slope and b represents the y-intercept.
By visually examining the scatter plot, we can see that the trend line passes through the points (1990, 250) and (2006, 339).
Using these two points, we can determine the equation of the trend line:
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (339 - 250) / (2006 - 1990)
m = 89 / 16
m ≈ 5.56
Next, let's find the y-intercept (b) using the slope-intercept form:
b = y - mx
Using the point (1990, 250):
250 = 5.56 * 1990 + b
250 = 11044 + b
b ≈ -10894
So, the equation of the trend line is:
y = 5.56x - 10894
To estimate the attendance at theme parks in the country in 2005, we substitute x=2005 into the equation:
y = 5.56 * 2005 - 10894
y ≈ 3054
Therefore, the estimated attendance at theme parks in the country in 2005 is approximately 3,054 million.