You have a job where you are helping track revenue and sales. Suppose that p is the price in dollars of a gadget and q = f(p) is the quantity sold (in hundreds). Then the revenue (in thousands of dollars) is given by R = p · f(p), depending on the price. Match the mathematical expression below with the best interpretation. I. f'(15)= 3 1. If the price increases from $15 to $16 then the company expects revenue to increase by about 3 thousand dollars. 2. If the price increases from $15 to $20 then the revenue will increase by about 60 thousand dollars. 3. If the price increases from $15 to $20 then the company expects to sell 3 hundred more gadgets. 4. When the company sells 3 hundred gadgets, the price is $60 each. 5. If the price increases from $15 to $16 then the company expects to sell about 3 hundred more gadgets. Your fellow intern claims that if f' (p) is negative then the revenue will decrease as well. In a sentence or two, briefly explain if this statement is necessarily true or not.
You have a job where you are helping track revenue and sales. Suppose that p is the price in dollars of a gadget and q = f(p) is the quantity sold (in hundreds). Then the revenue (in thousands of dollars) is given by R = p · f(p), depending on the price. Match the mathematical expression below with the best interpretation. I. f'(15)= 3 1. If the price increases from $15 to $16 then the company expects revenue to increase by about 3 thousand dollars. 2. If the price increases from $15 to $20 then the revenue will increase by about 60 thousand dollars. 3. If the price increases from $15 to $20 then the company expects to sell 3 hundred more gadgets. 4. When the company sells 3 hundred gadgets, the price is $60 each. 5. If the price increases from $15 to $16 then the company expects to sell about 3 hundred more gadgets. Your fellow intern claims that if f' (p) is negative then the revenue will decrease as well. In a sentence or two, briefly explain if this statement is necessarily true or not.
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.7: Direct And Inverse Variation
Problem 36PS
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Transcribed Image Text:You have a job where you are helping track revenue and sales. Suppose that p is the price in
dollars of a gadget and q = f(p) is the quantity sold (in hundreds). Then the revenue (in thousands
of dollars) is given by R = p · f(p), depending on the price. Match the mathematical expression
below with the best interpretation.
I. f' (15) = 3
1.
If the price increases from $15 to $16 then the company expects revenue to increase
by about 3 thousand dollars.
2.
If the price increases from $15 to $20 then the revenue will increase by about 60
thousand dollars.
3.
If the price increases from $15 to $20 then the company expects to sell 3 hundred
more gadgets.
When the company sells 3 hundred gadgets, the price is $60 each.
5.
If the price increases from $15 to $16 then the company expects to sell about 3
hundred more gadgets.
Your fellow intern claims that if f' (p) is negative then the revenue will decrease as well. In a
sentence or two, briefly explain if this statement is necessarily true or not.
4.
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