Based on the given data, it seems that the annual income is increasing steadily over the years.
To model this data, a linear function would be the most appropriate. A linear function takes the form of y = mx + b, where y is the income, x is the year, m is the slope, and b is the y-intercept.
To find the equation of the linear function, we can use the points (0, 18250) and (4, 20170):
Using the two points formula, we find the slope (m):
m = (20170 - 18250) / (4 - 0)
m = 1920 / 4
m = 480
Now, plug in the slope and one of the points into the formula to find the y-intercept (b):
18250 = 480(0) + b
b = 18250
Therefore, the linear function for the annual income would be:
y = 480x + 18250
To find the annual income in year 7 (x = 7), plug x = 7 into the equation:
y = 480(7) + 18250
y = 3360 + 18250
y = 21610
Therefore, the annual income for the theater in year 7 would be $21,610.
The table shows the annual income of a small theater company. Which type of function best models the data?
Year 0 1 2 3 4
Income ($) 18,250 18,730 19,210 19,090 20,170
What will be the annual income for the theater in year 7?
1 answer