Hello! Please help me with this questions. A+ answers only please. See attachment. I will greatly appreciate your help. Thank you!

 

 

Question 1 of 40
2.5 Points
Use the exponential growth model, A = A0ekt, to show that the time it takes a population to double (to
grow from A0 to 2A0 ) is given by t = ln 2/k.
A. A0 = A0ekt; ln = ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t
B. 2A0 = A0e; 2= ekt; ln = ln ekt; ln 2 = kt; ln 2/k = t
C. 2A0 = A0ekt; 2= ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t
D. 2A0 = A0ekt; 2 = ekt; ln 1 = ln ekt; ln 2 = kt; ln 2/k = toe
Question 2 of 40
2.5 Points
Evaluate the following expression without using a calculator.
Log7 √7
A. 1/4
B. 3/5
C. 1/2
D. 2/7
Question 3 of 40
2.5 Points
Use properties of logarithms to expand the following logarithmic expression as much as possible.
Logb (√xy3 / z3)
A. 1/2 logb x - 6 logb y + 3 logb z
B. 1/2 logb x - 9 logb y - 3 logb z
C. 1/2 logb x + 3 logb y + 6 logb z
D. 1/2 logb x + 3 logb y - 3 logb z
Question 4 of 40
2.5 Points
Use properties of logarithms to condense the following logarithmic expression. Write the expression as a
single logarithm whose coefficient is 1.
3 ln x – 1/3 ln y
A. ln (x / y1/2)
B. lnx (x6 / y1/3)
C. ln (x3 / y1/3)
D. ln (x-3 / y1/4)
Question 5 of 40
2.5 Points
Solve the following exponential equation. Express the solution set in terms of natural logarithms or
common logarithms to a decimal approximation, of two decimal places, for the solution.
32x + 3x - 2 = 0
A. {1}
B. {-2}
C. {5}
D. {0}
Question 6 of 40
2.5 Points
Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the
original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain
a decimal approximation, to two decimal places, for the solution.
2 log x = log 25 A. {12}
B. {5}
C. {-3}
D. {25}
Question 7 of 40
2.5 Points
Find the domain of following logarithmic function.
f(x) = log5 (x + 4)
A. (-4, ∞)
B. (-5, -∞)
C. (7, -∞)
D. (-9, ∞)
Question 8 of 40
2.5 Points
The graph of the exponential function f with base b approaches, but does not touch, the __________axis. This axis, whose equation is __________, is a __________ asymptote.
A. x; y = 0; horizontal
B. x; y = 1; vertical
C. -x; y = 0; horizontal
D. x; y = -1; vertical
Question 9 of 40
2.5 Points
Solve the following exponential equation. Express the solution set in terms of natural logarithms or
common logarithms to a decimal approximation, of two decimal places, for the solution.
ex = 5.7
A. {ln 5.7}; ≈1.74
B. {ln 8.7}; ≈3.74
C. {ln 6.9}; ≈2.49
D. {ln 8.9}; ≈3.97
Question 10 of 40
2.5 Points
The half-life of the radioactive element krypton-91 is 10 seconds. If 16 grams of krypton-91 are initially
present, how many grams are present after 10 seconds? 20 seconds?
A. 10 grams after 10 seconds; 6 grams after 20 seconds
B. 12 grams after 10 seconds; 7 grams after 20 seconds
C. 4 grams after 10 seconds; 1 gram after 20 seconds
D. 8 grams after 10 seconds; 4 grams after 20 seconds.
Question 11 of 40
2.5 Points
Write the following equation in its equivalent exponential form.
log6 216 = y
A. 6y = 216
B. 6x = 216
C. 6logy = 224
D. 6xy = 232
Question 12 of 40
2.5 Points
Write the following equation in its equivalent logarithmic form 2-4 = 1/16
A. Log4 1/16 = 64
B. Log2 1/24 = -4
C. Log2 1/16 = -4
D. Log4 1/16 = 54
Question 13 of 40
2.5 Points
Use properties of logarithms to expand the following logarithmic expression as much as possible.
logb (x2y)
A. 2 logy x + logx y
B. 2 logb x + logb y
C. logx - logb y
D. logb x – logx y
Question 14 of 40
2.5 Points
You have $10,000 to invest. One bank pays 5% interest compounded quarterly and a second bank pays
4.5% interest compounded monthly. Use the formula for compound interest to write a function for the
balance in each bank at any time t.
A. A = 20,000(1 + (0.06/4))4t; A = 10,000(1 + (0.044/14))12t
B. A = 15,000(1 + (0.07/4))4t; A = 10,000(1 + (0.025/12))12t
C. A = 10,000(1 + (0.05/4))4t; A = 10,000(1 + (0.045/12))12t
D. A = 25,000(1 + (0.05/4))4t; A = 10,000(1 + (0.032/14))12t.
Question 15 of 40
2.5 Points
The exponential function f with base b is defined by f(x) = __________, b > 0 and b ≠ 1. Using interval
notation, the domain of this function is __________ and the range is __________.
A. bx; (∞, -∞); (1, ∞)
B. bx; (-∞, -∞); (2, ∞)
C. bx; (-∞, ∞); (0, ∞)
D. bx; (-∞, -∞); (-1, ∞)
Question 16 of 40
2.5 Points
Write the following equation in its equivalent exponential form.
4 = log2 16
A. 2 log4 = 16
B. 22 = 4
C. 44 = 256
D. 24 = 16.
Question 17 of 40
2.5 Points
Find the domain of following logarithmic function.
f(x) = ln (x - 2)2
A. (∞, 2) ∪ (-2, -∞)
B. (-∞, 2) ∪ (2, ∞)
C. (-∞, 1) ∪ (3, ∞)
D. (2, -∞) ∪ (2, ∞).
Question 18 of 40
2.5 Points Use properties of logarithms to condense the following logarithmic expression. Write the expression as a
single logarithm whose coefficient is 1.
log x + 3 log y
A. log (xy)
B. log (xy3)
C. log (xy2)
D. logy (xy)3
Question 19 of 40
2.5 Points
An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e -0.000121t describes
the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 5715
years?
A. Approximately 7 grams
B. Approximately 8 grams
C. Approximately 23 grams
D. Approximately 4 grams.
Question 20 of 40
2.5 Points
Write the following equation in its equivalent logarithmic form.
3√8 = 2
A. Log2 3 = 1/8
B. Log8 2 = 1/3
C. Log2 8 = 1/2
D. Log3 2 = 1/8.
Question 21 of 40
2.5 Points
Many elevators have a capacity of 2000 pounds.
If a child averages 50 pounds and an adult 150 pounds, write an inequality that describes when x
children and y adults will cause the elevator to be overloaded.
A. 50x + 150y > 2000
B. 100x + 150y > 1000
C. 70x + 250y > 2000
D. 55x + 150y > 3000.
Question 22 of 40
2.5 Points
Write the partial fraction decomposition for the following rational expression.
6x - 11/(x - 1)2
A. 6/x - 1 - 5/(x - 1)2
B. 5/x - 1 - 4/(x - 1)2
C. 2/x - 1 - 7/(x - 1)
D. 4/x - 1 - 3/(x - 1).
Question 23 of 40
2.5 Points
Solve the following system.
x+y+z=6
3x + 4y - 7z = 1
2x - y + 3z = 5 A. {(1, 3, 2)}
B. {(1, 4, 5)}
C. {(1, 2, 1)}
D. {(1, 5, 7)
Question 24 of 40
2.5 Points
Write the form of the partial fraction decomposition of the rational expression.
5x2 - 6x + 7/(x - 1)(x2 + 1)
A. A/x - 2 + Bx2 + C/x2 + 3
B. A/x - 4 + Bx + C/x2 + 1
C. A/x - 3 + Bx + C/x2 + 1
D. A/x - 1 + Bx + C/x2 + 1
Question 25 of 40
2.5 Points
Solve the following system.
x=y+4
3x + 7y = -18
A. {(2, -1)}
B. {(1, 4)}
C. {(2, -5)}
D. {(1, -3)}.
Question 26 of 40
2.5 Points
Solve each equation by the substitution method.
x+y=1
x2 + xy – y2 = -5
A. {(4, -3), (-1, 2)}
B. {(2, -3), (-1, 6)}
C. {(-4, -3), (-1, 3)}
D. {(2, -3), (-1, -2).
Question 27 of 40
2.5 Points
Solve each equation by the substitution method.
y2 = x2 - 9
2y = x – 3
A. {(-6, -4), (2, 0)}
B. {(-4, -4), (1, 0)}
C. {(-3, -4), (2, 0)}
D. {(-5, -4), (3, 0)}.
Question 28 of 40
2.5 Points
On your next vacation, you will divide lodging between large resorts and small inns. Let x represent the
number of nights spent in large resorts. Let y represent the number of nights spent in small inns.
Write a system of inequalities that models the following conditions:
You want to stay at least 5 nights. At least one night should be spent at a large resort. Large resorts
average $200 per night and small inns average $100 per night. Your budget permits no more than $700
for lodging.
A. y≥1
x+y≥5
x≥1
300x + 200y ≤ 700
B.
y≥0
x+y≥3
x≥0
200x + 200y ≤ 700
C.
y≥1
x+y≥4
x≥2
500x + 100y ≤ 700
D.
y≥0
x+y≥5
x≥1
200x + 100y ≤ 700.
Question 29 of 40
2.5 Points
Write the partial fraction decomposition for the following rational expression.
x + 4/x2(x + 4)
A. 1/3x + 1/x2 - x + 5/4(x2 + 4)
B. 1/5x + 1/x2 - x + 4/4(x2 + 6)
C. 1/4x + 1/x2 - x + 4/4(x2 + 4)
D. 1/3x + 1/x2 - x + 3/4(x2 + 5)
Question 30 of 40
2.5 Points
Solve the following system by the substitution method.
{x + 3y = 8
{y = 2x - 9
A. {(5, 1)}
B. {(4, 3)}
C. {(7, 2)}
D. {(4, 3)}.
Question 31 of 40
2.5 Points
Let x represent one number and let y represent the other number. Use the given conditions to write a
system of equations. Solve the system and find the numbers.
The sum of two numbers is 7. If one number is subtracted from the other, their difference is -1. Find the
numbers.
A. x + y = 7; x - y = -1; 3 and 4
B. x + y = 7; x - y = -1; 5 and 6 C. x + y = 7; x - y = -1; 3 and 6
D. x + y = 7; x - y = -1; 2 and 3
Question 32 of 40
2.5 Points
Solve the following system by the substitution method.
{x + y = 4
{y = 3x
A. {(1, 4)}
B. {(3, 3)}
C. {(1, 3)}
D. {(6, 1)}
Question 33 of 40
2.5 Points
Write the partial fraction decomposition for the following rational expression.
ax +b/(x – c)2 (c ≠ 0)
A. a/a – c +ac + b/(x – c)2
B. a/b – c +ac + b/(x – c)
C. a/a – b +ac + c/(x – c)2
D. a/a – b +ac + b/(x – c)
Question 34 of 40
2.5 Points
Perform the long division and write the partial fraction decomposition of the remainder term.
x4 – x2 + 2/x3 - x2
A. x + 3 - 2/x - 1/x2 + 4x - 1
B. 2x + 1 - 2/x - 2/x + 2/x + 1
C. 2x + 1 - 2/x2 - 2/x + 5/x - 1
D. x + 1 - 2/x - 2/x2 + 2/x – 1
Question 35 of 40
2.5 Points
Solve each equation by either substitution or addition method.
x2 + 4y2 = 20
x + 2y = 6
A. {(5, 2), (-4, 1)}
B. {(4, 2), (3, 1)}
C. {(2, 2), (4, 1)}
D. {(6, 2), (7, 1)}.
Question 36 of 40
2.5 Points
A television manufacturer makes rear-projection and plasma televisions. The profit per unit is $125 for
the rear-projection televisions and $200 for the plasma televisions. Let x = the number of rear-projection televisions manufactured in a month and let y = the number of
plasma televisions manufactured in a month. Write the objective function that models the total monthly
profit.
A. z = 200x + 125y
B. z = 125x + 200y
C. z = 130x + 225y
D. z = -125x + 200y
Question 37 of 40
2.5 Points
Write the partial fraction decomposition for the following rational expression.
x2 – 6x + 3/(x – 2)3
A. 1/x – 4 – 2/(x – 2)2 – 6/(x – 2)
B. 1/x – 2 – 4/(x – 2)2 – 5/(x – 1)3
C. 1/x – 3 – 2/(x – 3)2 – 5/(x – 2)
D. 1/x – 2 – 2/(x – 2)2 – 5/(x – 2)3
Question 38 of 40
2.5 Points
Solve the following system by the addition method.
{4x + 3y = 15
{2x – 5y = 1
A. {(4, 0)}
B. {(2, 1)}
C. {(6, 1)}
D. {(3, 1)}
Question 39 of 40
2.5 Points
Find the quadratic function y = ax2 + bx + c whose graph passes through the given points.
(-1, -4), (1, -2), (2, 5)
A. y = 2x2 + x - 6
B. y = 2x2 + 2x - 4
C. y = 2x2 + 2x + 3
D. y = 2x2 + x – 5
Question 40 of 40
2.5 Points
Write the form of the partial fraction decomposition of the rational expression.
7x - 4/x2 - x - 12
A. 24/7(x - 2) + 26/7(x + 5)
B. 14/7(x - 3) + 20/7(x2 + 3)
C. 24/7(x - 4) + 25/7(x + 3)
D. 22/8(x - 2) + 25/6(x + 4)

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• 1492944153-College Algebra Exam5.docx