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?
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.