A movie store sells DVDs for $11 each. What is the cost C of n DVDs? Identify the situation as discrete or continuous.
a. C=11n;continuous
b. C=11+n;discrete
c. C=11+n;continuous
d. C=11n;discrete
a. C=11n; continuous
The correct answer is d. C = 11n; discrete.
In this situation, the cost of purchasing DVDs is determined by multiplying the number of DVDs (n) by the cost per DVD ($11). Since the number of DVDs must be a whole number (you can't purchase a fraction of a DVD), the situation is discrete.
The correct answer is option a. C=11n;continuous.
The formula C=11n represents the cost C of n DVDs, where 11 is the price of each DVD. In this situation, the cost is directly proportional to the number of DVDs. Multiplying the number of DVDs (n) by the cost of each DVD ($11) gives us the total cost (C). This formula represents a continuous situation since the cost can vary at any value of n, not limited to whole numbers.
Option b (C=11+n;discrete) is incorrect because adding the number of DVDs (n) to the cost of the first DVD ($11) does not accurately represent the total cost of n DVDs.
Option c (C=11+n;continuous) is incorrect because adding the number of DVDs (n) to the cost of the first DVD ($11) does not align with the situation described.
Option d (C=11n;discrete) is incorrect because multiplying the number of DVDs (n) by the cost of each DVD ($11) correctly represents the total cost of n DVDs, but this represents a continuous situation since the number of DVDs can be any positive real number, not limited to whole numbers.