The cost of sending an overnight package from Los Angeles to Miami is $25.00 for a package weighing up to but not including 1 pound and $3.50 for each additional pound or portion of a pound.Use the greatest integer function to create a model for the cost C of overnight delivery of a package weighing x pounds,x 0.
A)C = 25.00 - 3.50[[x]],x 0
B)C = 25.00 + 3.50[[x]],x 0
C)C = -25.00 + 3.50[[x]],x 0
D)С = -25.00 - 3.50 [[x]],x 0
E)C = 25.00[[x]] + 3.50,x 0

Question

The cost of sending an overnight package from Los Angeles to Miami is $25.00 for a package weighing up to but not including 1 pound and $3.50 for each additional pound or portion of a pound.Use the greatest integer function to create a model for the cost C of overnight delivery of a package weighing x pounds,x > 0. ​
A)​C = 25.00 - 3.50[[x]],x > 0
B)​C = 25.00 + 3.50[[x]],x > 0
C)​C = -25.00 + 3.50[[x]],x > 0
D)​С = -25.00 - 3.50 [[x]],x > 0
E)​C = 25.00[[x]] + 3.50,x > 0

Quizplus · Accepted Answer

The cost model starts with a base price of $25.00 for the first pound and adds $3.50 for each additional pound or fraction thereof. The greatest integer function, denoted by [[x]], rounds down to the nearest integer, which is not directly applicable here since we're dealing with additional pounds beyond the first. The correct model adds $3.50 for each pound beyond the first, hence the initial $25.00 plus $3.50 for each additional pound or part of a pound, represented as $25.00 + 3.50[[x-1]] for x > 1. However, since the choices do not explicitly show the adjustment for the first pound, the closest correct form is $25.00 + 3.50[[x]], understanding that the context implies handling the additional weight beyond the first pound.

The Cost of Sending an Overnight Package from Los Angeles