In 2012, the total student enrollment at Oxford University was 3976 undergraduate students. We also know that enrollment at Oxford grew during the decade 2010-2020 by an average of 133 students per year. This allows us to model the enrollment at Xavier over the time period 2010-2020.
(a) What function is being described here? That is, what output variable y is being described as depending on what input variable x? Describe the two variables and identify the units in which the quantities are being measured.
(b) Write down a linear equation that describes this relationship.
(c) Use your equation to estimate the student enrollment at Xavier in 2020. The actual value for the Fall 2020 semester was 4517 students; how close to this is your estimate?
In a certain city, the charge for commercial waste collection is $694.55 for 5 tons and $1098.32 for 8 tons.
(a) Find the equation of a linear function that, based on these two values, gives the cost C of waste collection in dollars as a function of the weight w in tons. Then sketch a graph of the function for weights of up to 10 tons; label your axes appropriately.
(b) What is the slope of this line? Report the number using appropriate units and interpret its meaning in the context of hauling this city's waste.