The revenue from the sale of x units of a commodity is r(x) Canadian dollars, and u(r) U.S. dollars is the equivalent value of r Canadian dollars. On September 8, 2009, $1 Canadian was worth $1.0764 U.S., and the rate of change of the U.S. dollar value was $0.925 U.S. per Canadian dollar. On the same day, sales were 470 units, producing revenue of $10,000 Canadian, and revenue was increasing by $4.2 Canadian per unit. Evaluate of the given expression on September 8, 2009, and write a sentence interpreting the value.
A) Canadian dollars per unit On September 8, 2009, revenue was increasing by 4.2 Canadian dollars per unit.
B) Canadian dollars per unit On September 8, 2009, revenue was increasing by 470 Canadian dollars per unit.
C) Canadian dollars per unit On September 8, 2009, revenue was decreasing by 8.4 Canadian dollars per unit.
D) Canadian dollars per unit On September 8, 2009, revenue was decreasing by 4.2 Canadian dollars per unit.
E) Canadian dollars per unit On September 8, 2009, revenue was increasing by 8.4 Canadian dollars per unit.

Question

The revenue from the sale of x units of a commodity is r(x) Canadian dollars, and u(r) U.S. dollars is the equivalent value of r Canadian dollars. On September 8, 2009, $1 Canadian was worth $1.0764 U.S., and the rate of change of the U.S. dollar value was $0.925 U.S. per Canadian dollar. On the same day, sales were 470 units, producing revenue of $10,000 Canadian, and revenue was increasing by $4.2 Canadian per unit. Evaluate  of the given expression on September 8, 2009, and write a sentence interpreting the value.
A) Canadian dollars per unit On September 8, 2009, revenue was increasing by 4.2 Canadian dollars per unit. 
B) Canadian dollars per unit On September 8, 2009, revenue was increasing by 470 Canadian dollars per unit. 
C) Canadian dollars per unit On September 8, 2009, revenue was decreasing by 8.4 Canadian dollars per unit. 
D) Canadian dollars per unit On September 8, 2009, revenue was decreasing by 4.2 Canadian dollars per unit. 
E) Canadian dollars per unit On September 8, 2009, revenue was increasing by 8.4 Canadian dollars per unit.

Quizplus · Accepted Answer

We need to find the derivative of u(r(x)) with respect to x, where r(x) is the revenue function in Canadian dollars. Using the chain rule, we get:
u'(r(x)) * r'(x)
The current exchange rate is u(1) = 1.0764, so u'(1) = 0.925. Also, r(470) = 10000, and r'(x) = 4.2. Therefore, the expression we need to evaluate is:
0.925 * 4.2 = 3.88
This means that for each unit sold, the revenue in U.S. dollars is increasing by $3.88. Since the exchange rate is fixed, this is equivalent to an increase of $4.2 in Canadian dollars per unit. Therefore, the answer is A.

The Revenue from the Sale of X Units of a Commodity