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Armstrong and Davis - Brief Calculus 3/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 6 / 30

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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1 2 3 4 5 6 7 8
1/1 –/5 –/2 –/1 –/6 1/2 4/8 –/5
Total
6/30 (20.0%)

  • Instructions

    Here are some textbook questions from Brief Calculus for the Business, Social, and Life Sciences 3/e by Bill Armstrong and Don Davis published by Jones & Bartlett Learning.

    Every problem includes a link to the appropriate section of a complete interactive eBook, (also available through a dynamic table of contents from the student's WebAssign homepage), allowing students to highlight and take notes as they read.

    Click here for a list of all of the questions coded in WebAssign. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

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1. 1/1 points  |  Previous Answers ArmsBrCalc3 3.1.013. My Notes
Question Part
Points
Submissions Used
1
1/1
1/50
Total
1/1
 
Determine the derivative for the given single-term function. When appropriate, simplify the derivative so that there are no negative or fractional exponents. A few helpful rules from algebra are:
(i) x−n = 
1
x n
, (ii) x m/n = 
nx m
.
f(x) = x7
f '(x) =
7x6
Correct: Your answer is correct.
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2. –/5 points ArmsBrCalc3 3.1.081. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
–/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50
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–/5
 
One group of voters that has received attention recently is Hispanic Americans. The number of Hispanic voters from 1995 to 2010 can be modeled by
f(x) = 1.08x + 11.7
    
0 ≤ x ≤ 15
where x represents the number of years since 1995 and
f(x)
 represents the number of Hispanic voters in millions.† Determine
f(3)
 and
f '(3).

f(3) = 
f '(3) = 


Interpret
f(3)
 and
f '(3).

In the year , the number of Hispanic voters was million, and increasing at a rate of million voters per year.
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3. –/2 points ArmsBrCalc3 3.2.041. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/50 0/50
Total
–/2
 
Complete the following.
f(x) = x2(x2 − 5)
(a) Determine the derivative.
f '(x) =


(b) Write the equation of the line tangent to the graph of the function at
x = 1.

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4. –/1 points ArmsBrCalc3 3.3.041. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Determine an equation of the line tangent to the graph of f at the indicated point.
f(x) = (3x − 1)3; (1, 8)
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5. –/6 points ArmsBrCalc3 3.3.083. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
–/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50
Total
–/6
 
A sociological topic that has been discussed since the end of World War II is the status of women in the labor force. The number of unmarried women in the U.S. labor force from 1970 to 2010 can be modeled by
f(x) = 1.11(1.57x + 17.27)0.66
    
0 ≤ x ≤ 40
where x represents the number of years since 1970 and
f(x)
 represents the number of unmarried women in the U.S. labor force, measured in millions.†
(a) Determine
f '(x).

f '(x) =


(b) Evaluate
f(35) and f '(35).
 (Round your answers to two decimal places.)
f(35) = 
f '(35) = 


Interpret
f(35) and f '(35).

In the year , the approximate number of unmarried women in the labor force was million and was increasing by million women per year.
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6. 1/2 points  |  Previous Answers ArmsBrCalc3 3.4.031. My Notes
Question Part
Points
Submissions Used
1 2
0/1 1/1
2/50 2/50
Total
1/2
 
Evaluate Δy and dy for the function using the given x and dx values. (Round your answers to four decimal places.)
f(x) = 
x2 + 1
x2 − 1
, x = 4, Δx = dx = 0.2
Δy =  Incorrect: Your answer is incorrect.
dy =  Correct: Your answer is correct.
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7. 4/8 points  |  Previous Answers ArmsBrCalc3 3.5.007. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8
–/1 –/1 –/1 1/1 –/1 1/1 1/1 1/1
0/50 0/50 0/50 1/50 0/50 1/50 1/50 1/50
Total
4/8
 
Assume the cost function
C(x)
 is measured in dollars. Complete the following.
C(x) = 27x + 5200
(a) Determine the marginal cost function MC.
MC(x) =
27


(b) Evaluate
MC(x)
 for the production level
x = 20.

MC(20) =


Interpret
MC(20).
The estimated cost of producing the unit is $ Correct: Your answer is correct. .

(c) Evaluate the actual change in cost by evaluating
C(x + 1) − C(x)
 when
x = 20.

C(21) − C(20) =


Compare with the answer in part (b).
The actual cost of producing the Correct: Your answer is correct. unit is $ Correct: Your answer is correct. . This is Correct: Your answer is correct. our estimate in part (b).
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8. –/5 points ArmsBrCalc3 3.5.026. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
–/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50
Total
–/5
 
The financial planning team at a certain company determines that the profit function for producing and selling its bobbleheads can be modeled by
P(x) = −0.001x2 + 7x − 5000    0 ≤ x ≤ 7000
where x represent the number of bobbleheads produced and sold and
P(x)
 represents the monthly profit in dollars.
(a) Determine MP, the marginal profit function.
MP =


Evaluate MP(2000).
MP(2000) =


Interpret MP(2000).
The estimated monthly profit of producing and selling the bobblehead is $ .

(b) If the company is producing and selling 2000 bobbleheads per month, is profit increasing or decreasing?
    
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