Write A Piecewise Function From Word Problem: shipping company's rates

josephine_mcr

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Shipping company IPS has shipping rates that are a function of the weight of the parcel. For packages weighing less than or equal to 5 pounds, they charge $1.25 per pound. For packages weighing between 5 and 18 pounds, they charge $2.25 per pound. If packages weigh 18 pounds or more, they charge $3.25 per pound. IPS refuses to ship any parcel weighing more than 68 pounds. There is also a flat fee of $3 for all deliveries and an additional fee of $5 for all deliveries weighing 18 pounds or more.

Complete the following description of a piecewise function so that it describes the shipping costs C(x)
C(x) in dollars as a function of the weight xx in pounds.

C(x) =

{
??? if x is in the interval (0, 5]
{
??? if x is in the interval (5, 18)
{
??? if x is in the interval [18, 68]

 
Shipping company IPS has shipping rates that are a function of the weight of the parcel. For packages weighing less than or equal to 5 pounds, they charge $1.25 per pound. For packages weighing between 5 and 18 pounds, they charge $2.25 per pound. If packages weigh 18 pounds or more, they charge $3.25 per pound. IPS refuses to ship any parcel weighing more than 68 pounds. There is also a flat fee of $3 for all deliveries and an additional fee of $5 for all deliveries weighing 18 pounds or more.

Complete the following description of a piecewise function so that it describes the shipping costs C(x)
in dollars as a function of the weight x in pounds.

C(x) =

{
??? if x is in the interval (0, 5]
{
??? if x is in the interval (5, 18)
{
??? if x is in the interval [18, 68]


Take it one step at a time. Here's the first part:

For packages weighing less than or equal to 5 pounds, they charge $1.25 per pound.

Now answer: if the weight in pounds, x, is between 0 and 5, what is the shipping cost, C(x)?
 
Take it one step at a time. Here's the first part:
For packages weighing less than or equal to 5 pounds, they charge $1.25 per pound.

Now answer: if the weight in pounds, x, is between 0 and 5, what is the shipping cost, C(x)?

Would it be...$6.25 (5 * 1.25) ?
 
Would it be...$6.25 (5 * 1.25) ?
But your result is a constant. Shouldn't the cost of shipping a 3lb package be different from shipping a 5lb package? Where is the flat fee of $3 for all deliveries??

Try figuring out the cost for x=1lb, x=2lbs, x=3lbs ...(do not go past 5lbs) until you see a pattern.
 
Would it be...$6.25 (5 * 1.25) ?

Given just the small part of the problem that I quoted (ignoring the later mention of the flat fee), what you have done is correct only when the weight is 5 pounds. But I asked about a weight of x pounds, if you know that is less than or equal to 5. For that, you need to write an expression (which will be part of the final answer). What is that expression?
 
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