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Crauder et al - Functions and Change 5/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 4 / 52

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

Last Saved : n/a Saving...  ()

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4/5 –/28 –/8 –/3 –/7 –/1
Total
4/52 (7.7%)

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    Create your course assignments by selecting questions from our bank of end-of-section exercises, as well as enhanced interactive examples with videos.

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    In this assignment we present several textbook question types found in Functions and Change: A Modeling Approach to College Algebra 5/e by Bruce Crauder, Benny Evans, and Alan Noell published by Cengage Learning.

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1. 4/5 points  |  Previous Answers CraudColAlg5 2.1.EX.010.MI. My Notes
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The profit P, in thousand of dollars, that a manufacturer makes is a function of the number N of items produced in a year, and the formula is as follows.
P = −0.2N2 + 3.6N − 9
(a) Express using functional notation the profit at a production level of 3 items per year.
P( Correct: Your answer is correct. )

Calculate that value.
Correct: Your answer is correct. thousand dollars

(b) Determine the two break-even points for this manufacturer—that is, the two production levels at which the profit is zero.
N = Correct: Your answer is correct. (smaller value)
N = Correct: Your answer is correct. (larger value)

(c) Determine the maximum profit if the manufacturer can produce at most 17 in a year.
Incorrect: Your answer is incorrect. thousand dollars

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2. –/28 points CraudColAlg5 2.1.EX.014.MI. My Notes
Question Part
Points
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–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
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–/28
 
Suppose you borrow P dollars at a monthly interest rate of r (as a decimal) and wish to pay off the loan in t months. Then your monthly payment can be calculated using the following formula in dollars.
M = 
Pr(1 + r)t
(1 + r)t − 1
 
Remember that for monthly compounding, you get the monthly rate by dividing the APR by 12. Suppose you borrow $4200 at 9% APR (meaning that you use r = 0.09/12 in the preceding formula) and pay it back in 2 years.
(a) What is your monthly payment? (Round your answer to the nearest cent.)
$

(b) Lets look ahead to the time when the loan is paid off. (Round your answers to the nearest cent.)
(i) What is the total amount you paid to the bank?
$

(ii) How much of that was interest?
$
(c) The amount B that you still owe the bank after making k monthly payments can be calculated using the variables r, P, and t. The relationship is given by the formula below in dollars.
B = P × 
(1 + r)t − (1 + r)k
(1 + r)t − 1
 
(i) How much do you still owe the bank after 1 year of payments? (Round your answer to the nearest cent.)
$

(ii) An amortization table is a table that shows how much you still owe the bank after each payment. Complete the amortization table for this loan. (Round your answers to the nearest cent.)
Number of
payments made 		Amount still owed
(in dollars) 		Number of
payments made 		Amount still owed
(in dollars)
0 4200.00 13
1 14
2 15
3 16
4 17
5 18
6 19
7 20
8 21
9 22
10 23
11 24
12

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3. –/8 points CraudColAlg5 2.2.EX.009.alt. My Notes
Question Part
Points
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–/8
 
The growth G of a population over a week is a function of the population size n at the beginning of the week. If both n and G are measured in thousands of animals, the formula is as follows.
G = −0.25n2 + 5n
(a) Make a graph of G versus n. Include values of n up to 25 thousand animals.



(b) Use functional notation to express the growth over a week if the population at the beginning is 3 thousand animals.
G


Calculate that value.
thousand animals

(c) Calculate G(24).
G(24) =

Explain in practical terms what your answer means.
    

(d) For what values of n is the function G increasing? (Enter your answer using interval notation.)
n =


Determine whether the graph is concave up or concave down for these values.
    

Explain in practical terms what this means.
    
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4. –/3 points CraudColAlg5 2.4.SB.010. My Notes
Question Part
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–/3
 
Use the crossing-graphs method to solve the given equation. There are three solutions. Find all three. (Round your answers to two decimal places.)
x4 = 3x
x =  (smallest value)
x = 
x =  (largest value)
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5. –/7 points CraudColAlg5 2.6.EX.007.MI. My Notes
Question Part
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–/7
 
We want to form a rectangular pen of area 160 square feet. One side of the pen is to be formed by an existing building and the other three sides by a fence. (See the figure below.) Let W be the length, in feet, of the sides of the rectangle perpendicular to the building, and let L be the length, in feet, of the other side.
(a) Find a formula for the total amount of fence F needed in terms of W and L.
F =


(b) Express, as an equation involving W and L, the requirement that the total area formed be 160 square feet.


(c) Solve the equation you found in part (b) for L.
L =


(d) Use your answers to parts (a) and (c) to find a formula for F, the total amount, in feet, of fence needed, as a function of W alone.
F =


(e) Make a graph of F versus W.


(f) Determine the dimensions of the rectangle that requires a minimum amount of fence. (Round your answers to two decimal places.)
W = ft
L = ft

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6. –/1 points CraudColAlg5 2.AFL2.001. My Notes
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–/1
 
Refer to the graph of f in the figure below.
Sketch the graph of the following function.
Shifting:    
f(x + 6)
No Solution
Help
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