Question

1. The table shows the Total Expenses y (in dollars) of the College or University for year 2020-2021 and 2021-2022. Mine it's 21,211

a) Write a function that represents the Total Expenses y (in dollars) of that College or University you would like to attend after t years.

b) Use the function to estimate the Total Expenses your first year of school. *This year (t) is not the same for everyone since there are 8th graders to 11th graders in the class.



c) Sketch a graph (by hand) to model your function.


d) Identify the y-intercept and asymptotes of the graph. Find the domain and range of your function. Then describe the end behavior of the function.

Answer 1

a) We can use the given data to find the rate of change (slope) of the expenses over one year, and then use it to write the equation of a line in slope-intercept form:

Slope m = (Total Expenses in 2021-2022 - Total Expenses in 2020-2021) / 1 year

m = (23,500 - 21,211) / 1 = 2,289

Using the point-slope form of a line, we can write the equation as:

y - 21,211 = 2,289(t - t1), where t1 is the year 2020-2021.

Simplifying, we get:

y = 2,289t + 18,922

b) To estimate the Total Expenses for your first year of school, you need to know what year you will start. Let's say you will start in 2024-2025, which is 3 years from 2021-2022.

Then, plugging in t = 3 into the equation we just found, we get:

y = 2,289(3) + 18,922 = 23,789

So the estimated Total Expenses for your first year of school would be $23,789.

c) The graph of the function y = 2,289t + 18,922 is a straight line with a positive slope of 2,289. It passes through the point (0, 18,922) on the y-axis, and it will extend indefinitely in both directions.

d) The y-intercept of the graph is the point (0, 18,922), which represents the Total Expenses for the year 2020-2021. There are no vertical asymptotes, but the graph will approach a horizontal asymptote as t goes to infinity, since the expenses cannot increase indefinitely. The domain of the function is all real numbers, and the range is all values greater than or equal to 18,922. As t increases, the function increases without bound, so the end behavior is that the graph goes up to the right.