Isabella sells homemade birthday cakes for a profit of $39 per cake. She is considering a new recipe that will allow her to make more money. Her new profit could be expressed by the function y = 45x, where x is the number of cakes sold and y is the amount of profit.

Question

Part A: How many more dollars will Isabella earn on each cake if she switches to the new material? Explain or show how you determined this.

Part B: Write a list of six ordered pairs for y = 45x, showing the output as the amount of profit when the input is the number of cakes sold. Explain how this list proves the equation is a function.

Answer 1

Part A: To determine how many more dollars Isabella will earn on each cake with the new material, we can subtract the old profit per cake from the new profit per cake:

New Profit per Cake: $45
Old Profit per Cake: $39

New profit per cake - Old profit per cake = $45 - $39 = $6

So, Isabella will earn $6 more on each cake if she switches to the new material.

Part B:
List of ordered pairs for y = 45x:

(1, 45)
(2, 90)
(3, 135)
(4, 180)
(5, 225)
(6, 270)

This list of ordered pairs proves that the equation y = 45x is a function because each input (the number of cakes sold) corresponds to exactly one output (the amount of profit). In other words, for each value of x, there is only one corresponding value of y, which is a key characteristic of a function.