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The function
C gives the cost, in dollars, to shred
w pounds of confidential documents of a company.
What is the best interpretation for the following statement?

C^(')(500)=80
Choose 1 answer:
(A) The cost to shred documents, when the weight of the documents is 500 pounds, is increasing at a rate of
$80 per pound.
(B) The average cost to shred documents is
(80)/(500) dollars per pound.
(C) The cost to shred 500 pounds of documents is
$80.
(D) The cost to shred documents, when the weight of the documents is 500 pounds, is increasing at a rate of
$80.

The function $C$ gives the cost, in dollars, to shred $w$ pounds of confidential documents of a company. $\newline$ What is the best interpretation for the following statement? $\newline$ $C^{\prime}(500)=80$ $\newline$ Choose $1$ answer: $\newline$ (A) The cost to shred documents, when the weight of the documents is $500$ pounds, is increasing at a rate of $\$ 80$ per pound. $\newline$ (B) The average cost to shred documents is $\frac{80}{500}$ dollars per pound. $\newline$ (C) The cost to shred $500$ pounds of documents is $\$ 80$ . $\newline$ (D) The cost to shred documents, when the weight of the documents is $500$ pounds, is increasing at a rate of $\$ 80$ .

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Evaluate two-variable equations: word problems

Full solution

Q. The function

C

gives the cost, in dollars, to shred

w

pounds of confidential documents of a company.

\newline

What is the best interpretation for the following statement?

\newline

C^{\prime}(500)=80

\newline

Choose

1

answer:

\newline

(A) The cost to shred documents, when the weight of the documents is

500

pounds, is increasing at a rate of

\$ 80

per pound.

\newline

(B) The average cost to shred documents is

\frac{80}{500}

dollars per pound.

\newline

(C) The cost to shred

500

pounds of documents is

\$ 80

.

\newline

(D) The cost to shred documents, when the weight of the documents is

500

pounds, is increasing at a rate of

\$ 80

.

Cost Function Derivative: $C'(500)$ refers to the derivative of the cost function at $500$ pounds, which indicates the rate of change of the cost with respect to the weight of the documents.
Rate of Cost Change: Since $C'(500)$ is the rate of change of cost, it means that the cost is increasing by $\$80$ for each additional pound of documents when the weight is at $500$ pounds.
Interpretation of $C'(500)=80$ : Therefore, the correct interpretation of the statement $C'(500)=80$ is that the cost to shred documents is increasing at a rate of $\$80$ per pound when the weight of the documents is $500$ pounds.

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