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
a. Linear
b. Exponential
c. Quadratic
What will be the annual income for the theater in year 7?
To determine which type of function best models the data, we can analyze the pattern of the income values over the years.
In this case, the income values do not appear to follow a linear or quadratic pattern as they do not increase by a consistent amount each year or follow a parabolic shape.
Instead, the income values show a somewhat exponential pattern where the income generally increases each year, but the rate of increase is not constant. Therefore, an exponential function would best model the data.
To find the annual income for the theater in year 7, we can use the exponential function to predict the income. One possible exponential function that could model the data is:
Income = a * (r)^t
Where:
- Income is the amount in dollars
- a is the initial value of income (Income in year 0)
- r is the growth rate
- t is the number of years
From the given data, we can determine the initial income value (a = 18,250) and calculate the growth rate (r) by looking at the percentage change in income from year to year.
By using this exponential function with the determined growth rate, we can find the income for the theater in year 7.