Inactive Tutor answered • 10/07/21
Hi Monica.
An interesting question:
The following graph shows the average retail price of regular gasoline in Tucson and Albuquerque over a 1-month period. Suppose T(d) represents the price of gas in Tucson as a function of the day, and A(d) represents the price of gas in Albuquerque as a function of the day.
A) Consider the function (T−A)(d). What does it mean in practical terms if (T−A)(d) is…
A1) positive?
A2) negative?
A3) zero?
B) Using the graphs below, determine the following:
B1) On what day(s) does (T−A)(d)=0?
B2) What is the lowest/most negative value of (T−A)(d)? On what date does that occur?
B3) What is the largest/most positive value of (T−A)(d)? On what date does that occur?
Let's suppose you live exactly halfway between Tucson and Albuquerque and you could buy gas in either city. Obviously, you will want to buy the cheapest gas at any point in time.
To answer this part of your question:
A) Consider the function (T−A)(d). What does it mean in practical terms if (T−A)(d) is…
A1) positive?
Since on Day d, (T-A) is positive, the price of gas is higher in Tucson and you will buy your gas in Albuquerque
A2) negative?
Since on Day d, (T-A) is negative, the price of gas is higher in Albuquerque and you will buy your gas in Tucson
A3) zero?
Since on Day d, (T-A) is zero, theere is no difference in the price of gas in either city and you will buy your gas where ever you like
The answers to Part B come straight from reading the graph, which is too small for an old lady like me to read. However, :
B1) On what day(s) does (T−A)(d)=0?
Would be any place on the graph where the 2 lines cross. I think I see 2, but double check.
B2) What is the lowest/most negative value of (T−A)(d)? On what date does that occur?
If Albuquerque is red and Tucson is blue, then (T-A) is most negative when to red line is highest over the blue one. That happens to the left of the center of the graph.
B3) What is the largest/most positive value of (T−A)(d)? On what date does that occur?
Again, if Albuquerque is red and Tucson is blue, then (T-A) is most positive when to blue line is highest over the red one. That looks to be on the far right of the graph.
Good Luck!
