A drive-in theatre sells entrance tickets for cars on weekend nights. At capacity, the drive-in can hold 72 cars. The function c(n) = 25n represents the drive-in's revenue on a weekend night, where n represents the number of cars. In this situation, what is the domain of c(n)?
a) all real numbers
b) all positive rational numbers
c) all positive integers less than or equal to 72
d) all positive integers that are multiples of 25
Show your work
The domain of a function represents all possible inputs or values that the function can take. In this case, the function c(n) represents the revenue generated by selling entrance tickets for cars. Therefore, the inputs or values for the function c(n) should be the possible number of cars that can enter the drive-in.
According to the given information, the drive-in can hold 72 cars at capacity. Therefore, the number of cars should be less than or equal to 72.
The domain of c(n) would be all positive integers less than or equal to 72.
Therefore, the correct answer is c) all positive integers less than or equal to 72.
Could you show your work.
Certainly!
The function c(n) = 25n represents the drive-in's revenue on a weekend night, where n represents the number of cars.
To find the domain of c(n), we need to consider what values n can take.
Given that the drive-in can hold a maximum of 72 cars, the number of cars (n) should be less than or equal to 72.
So, the domain of c(n) is all positive integers less than or equal to 72.
Mathematically, we can represent this as:
Domain of c(n) = {n | n ≤ 72}
Therefore, the correct answer is c) all positive integers less than or equal to 72.
Is there another option you can show your work differently?
Sure! Here's another way to show the work:
The function c(n) = 25n represents the drive-in's revenue on a weekend night, where n represents the number of cars.
To find the domain of c(n), we need to determine the possible values for n. In this case, n represents the number of cars that can enter the drive-in.
According to the information given, the drive-in can hold a maximum of 72 cars at capacity. This means that the number of cars, n, should be less than or equal to 72.
So, the domain of c(n) would be all values of n that satisfy this condition:
n ≤ 72
To simplify further, we can consider that n represents a positive whole number (integer), as it would not make sense to have a fractional or negative number of cars.
Thus, the domain of c(n) is the set of all positive integers less than or equal to 72.
Mathematically, we can represent this as:
Domain of c(n) = {1, 2, 3, ..., 72}
Therefore, the correct answer is c) all positive integers less than or equal to 72.