Question

interpreting function notation let c(t) be the number of customers in a restaurant t hours after 8 a.m. explain the meaning of each statement. (see example 2.) a. c(10)=0 b. c(3)=c(8) c. c(4)=29 d. c(13.5)<c(12)

Explanation:

a. \(c(0)=0\) means that 0 hours after 8 a.m. (i.e., at 8 a.m.), there are 0 customers in the restaurant.
b. \(c(3)=c(8)\) means that the number of customers in the restaurant 3 hours after 8 a.m. (i.e., at 11 a.m.) is the same as the number of customers 8 hours after 8 a.m. (i.e., at 4 p.m.).
c. \(c(n)=29\) means that \(n\) hours after 8 a.m., there are 29 customers in the restaurant.
d. \(c(13.5)<c(12)\) means that the number of customers 13.5 hours after 8 a.m. (i.e., at 9:30 p.m.) is less than the number of customers 12 hours after 8 a.m. (i.e., at 8 p.m.).

Answer:

a. At 8 a.m., there are 0 customers in the restaurant.
b. The number of customers at 11 a.m. is the same as at 4 p.m.
c. \(n\) hours after 8 a.m., there are 29 customers in the restaurant.
d. The number of customers at 9:30 p.m. is less than at 8 p.m.