Reason Abstractly Refer to the conversions in the tables below.

a. Write a function for each table.

b. If you graph the points, the graph for which function would have the steepest slope? Justify your response.

c. Which function has the least rate of change? Explain.

Model with Mathematics Write a real-world problem where you would want to compare rates of change for two different functions.

Persevere with Problems Explain why the graph of the function \(\text{y} = 3\text{x} + 40\) will never intersect the graph of the function \(\text{y} = 3\text{x} + 35\).

Reason Inductively The exchange rate to convert U.S. dollars to British pounds is represented by the function \(\text{p} = 0.61\text{d}\) where p is the amount in pounds and d is the number of dollars. One U.S. dollar can also be exchanged for 0.69 European euro. If you exchange $250 for pounds and $250 for euros, which of the following is true? _____

I. You will receive 152.5 pounds and 172.5 euros.

II. You will receive about 410 pounds and about 362 euros.

III. You will receive 250 dollars.

IV. You will receive the same amount of pounds and euros.