Question

let ( c(t) ) be the number of customers in a restaurant ( t ) hours after 8 a.m. match each statement with its meaning
( c(0)=0 )
( c(3)=c(8) )
( c(n)=29 )
( c(13)<c(12) )
there are no customers in the restaurant at midnight. there are no customers in the restaurant at 8 a.m.
there are 29 customers in the restaurant ( n ) hours after 8 a.m.
there are ( n ) customers in the restaurant 29 hours after 8 a.m.
there are fewer customers in the restaurant at 1:00 p.m. than there are at noon.

Explanation:

• For \(c(0) = 0\): At \(t = 0\) (which is 8 A.M.), the number of customers \(c(t)\) is 0. So it means "There are no customers in the restaurant at 8 A.M."
• For \(c(3)=c(8)\): Since \(t = 3\) corresponds to 11 A.M. (\(8 + 3=11\)) and \(t = 8\) corresponds to 4 P.M. (\(8+8 = 16\) or 4 P.M. in 12 - hour format), it means the number of customers at 11 A.M. is equal to the number of customers at 4 P.M.
• For \(c(n)=29\): By the definition of the function \(c(t)\) (where \(t\) is hours after 8 A.M.), it means "There are 29 customers in the restaurant \(n\) hours after 8 A.M."
• For \(c(13)\lt c(12)\): \(t = 12\) corresponds to 8 P.M. (\(8+12 = 20\) or 8 P.M.) and \(t = 13\) corresponds to 9 P.M. (\(8 + 13=21\) or 9 P.M.). So it means "There are fewer customers in the restaurant at 9 P.M. than there are at 8 P.M."

Answer:

• \(c(0)=0\): There are no customers in the restaurant at 8 A.M.
• \(c(3)=c(8)\): The number of customers at 11 A.M. is equal to the number of customers at 4 P.M.
• \(c(n)=29\): There are 29 customers in the restaurant \(n\) hours after 8 A.M.
• \(c(13)\lt c(12)\): There are fewer customers in the restaurant at 9 P.M. than there are at 8 P.M.