C 957 | C957 Exam 4: Applied Algebra Updated and
Latest Questions and Correct Answers with
Rationale - WGU
1. Which of the following functions represents an initial population of 500 growing by 8%
annually?
A. f(x) = 500(0.08)^x
B. f(x) = 8(500)^x
C. f(x) = 500(1.08)^x
D. f(x) = 500 + 1.08x
Correct Answer: C
Explanation: This question asks for an exponential growth model based on a percentage
increase. The standard form for exponential growth is f(x) = a(1 + r)^x, where ‘a’ is the
initial value. In this case, the initial value is 500 and the growth rate is 0.08. Adding the
growth rate to 1 gives a growth factor of 1.08. Therefore, the correct function is f(x) =
500(1.08)^x as shown in option B.
2. Solve for x in the equation: log3(x) = 4.
A. x = 12
B. x = 81
C. x = 64
D. x = 7
Correct Answer: B
Explanation: To solve a basic logarithmic equation, we convert it into its equivalent
exponential form. The base of the logarithm is 3 and the result is the exponent. Thus, the
equation becomes x = 3 to the power of 4. Calculating 3 times 3 times 3 times 3 results in
81. This conversion demonstrates the fundamental relationship between logs and
exponents.
3. What is the value of x in the radical equation sqrt(2x + 1) = 5?
A. x = 2
B. x = 12
C. x = 24
D. x = 13
,Correct Answer: B
Explanation: The first step in solving this radical equation is to square both sides to
eliminate the square root. Squaring 5 results in 25, so the equation becomes 2x + 1 = 25.
Next, we subtract 1 from both sides to get 2x = 24. Dividing both sides by 2 yields the final
answer of 12. Plugging 12 back into the original equation confirms that the square root of
25 is indeed 5.
4. If a $1,000 investment earns 5% interest compounded continuously, which formula
represents the balance after t years?
A. A = 1000(1.05)^t
B. A = 1000 + 0.05t
C. A = 1000(1 + 0.05/1)^t
D. A = 1000e^(0.05t)
Correct Answer: D
Explanation: Continuous compounding requires the use of the mathematical constant ‘e’.
The standard formula for continuous growth is A = Pe^(rt), where P is the principal
amount. Here, the principal P is 1000 and the rate r is 0.05. Substituting these values into
the formula gives A = 1000e^(0.05t). This model assumes interest is added at every
possible instant throughout the year.
5. Solve for x: 2^(x+1) = 32.
A. x = 5
B. x = 4
C. x = 16
D. x = 6
Correct Answer: B
Explanation: This exponential equation can be solved by expressing both sides with a
common base. Since 32 is equal to 2 raised to the 5th power, we rewrite the equation as
2^(x+1) = 2^5. With the bases equal, we can set the exponents equal to each other,
resulting in x + 1 = 5. Subtracting 1 from both sides gives us the value of x as 4. This method
is the most efficient way to solve exponential equations when the base is a power of the
other side.
6. Simplify the expression: (x8)(1/2).
A. x^4
B. x^16
C. x^6
, D. x^10
Correct Answer: A
Explanation: This problem involves applying the power of a power rule for exponents. The
rule states that (am)n = a^(m*n), meaning we multiply the exponents. In this specific case,
we multiply 8 by 1/2 to simplify the expression. The calculation 8 times 0.5 results in an
exponent of 4. Therefore, the simplified form of the radical expression is x^4.
7. A substance has a half-life of 10 years. If you start with 100 grams, which expression
represents the amount remaining after 30 years?
A. 100(0.5)^30
B. 100(0.5)^3
C. 100(2)^3
D. 30(0.5)^10
Correct Answer: B
Explanation: Half-life problems utilize an exponential decay model with a base of 0.5. The
exponent represents the number of half-life periods that have passed, calculated as total
time divided by half-life duration. After 30 years, exactly 3 half-life periods of 10 years each
have occurred. Substituting these values into the decay formula yields 100(0.5)^3. This
correctly models the reduction of the substance over the specified timeframe.
8. Which property of logarithms is represented by log(ab) = log(a) + log(b)?
A. Power Property
B. Quotient Property
C. Identity Property
D. Product Property
Correct Answer: D
Explanation: The Product Property of logarithms states that the log of a product is equal to
the sum of the logs of its factors. This is a fundamental rule used to expand or condense
logarithmic expressions. In the expression log(ab), ‘a’ and ‘b’ are being multiplied, which is
a product. By applying this property, the expression is rewritten as the sum log(a) + log(b).
Understanding these properties is essential for solving complex algebraic equations
involving logs.
9. Solve for x: sqrt(x - 4) + 2 = 6.
A. x = 8
B. x = 20
C. x = 12
Latest Questions and Correct Answers with
Rationale - WGU
1. Which of the following functions represents an initial population of 500 growing by 8%
annually?
A. f(x) = 500(0.08)^x
B. f(x) = 8(500)^x
C. f(x) = 500(1.08)^x
D. f(x) = 500 + 1.08x
Correct Answer: C
Explanation: This question asks for an exponential growth model based on a percentage
increase. The standard form for exponential growth is f(x) = a(1 + r)^x, where ‘a’ is the
initial value. In this case, the initial value is 500 and the growth rate is 0.08. Adding the
growth rate to 1 gives a growth factor of 1.08. Therefore, the correct function is f(x) =
500(1.08)^x as shown in option B.
2. Solve for x in the equation: log3(x) = 4.
A. x = 12
B. x = 81
C. x = 64
D. x = 7
Correct Answer: B
Explanation: To solve a basic logarithmic equation, we convert it into its equivalent
exponential form. The base of the logarithm is 3 and the result is the exponent. Thus, the
equation becomes x = 3 to the power of 4. Calculating 3 times 3 times 3 times 3 results in
81. This conversion demonstrates the fundamental relationship between logs and
exponents.
3. What is the value of x in the radical equation sqrt(2x + 1) = 5?
A. x = 2
B. x = 12
C. x = 24
D. x = 13
,Correct Answer: B
Explanation: The first step in solving this radical equation is to square both sides to
eliminate the square root. Squaring 5 results in 25, so the equation becomes 2x + 1 = 25.
Next, we subtract 1 from both sides to get 2x = 24. Dividing both sides by 2 yields the final
answer of 12. Plugging 12 back into the original equation confirms that the square root of
25 is indeed 5.
4. If a $1,000 investment earns 5% interest compounded continuously, which formula
represents the balance after t years?
A. A = 1000(1.05)^t
B. A = 1000 + 0.05t
C. A = 1000(1 + 0.05/1)^t
D. A = 1000e^(0.05t)
Correct Answer: D
Explanation: Continuous compounding requires the use of the mathematical constant ‘e’.
The standard formula for continuous growth is A = Pe^(rt), where P is the principal
amount. Here, the principal P is 1000 and the rate r is 0.05. Substituting these values into
the formula gives A = 1000e^(0.05t). This model assumes interest is added at every
possible instant throughout the year.
5. Solve for x: 2^(x+1) = 32.
A. x = 5
B. x = 4
C. x = 16
D. x = 6
Correct Answer: B
Explanation: This exponential equation can be solved by expressing both sides with a
common base. Since 32 is equal to 2 raised to the 5th power, we rewrite the equation as
2^(x+1) = 2^5. With the bases equal, we can set the exponents equal to each other,
resulting in x + 1 = 5. Subtracting 1 from both sides gives us the value of x as 4. This method
is the most efficient way to solve exponential equations when the base is a power of the
other side.
6. Simplify the expression: (x8)(1/2).
A. x^4
B. x^16
C. x^6
, D. x^10
Correct Answer: A
Explanation: This problem involves applying the power of a power rule for exponents. The
rule states that (am)n = a^(m*n), meaning we multiply the exponents. In this specific case,
we multiply 8 by 1/2 to simplify the expression. The calculation 8 times 0.5 results in an
exponent of 4. Therefore, the simplified form of the radical expression is x^4.
7. A substance has a half-life of 10 years. If you start with 100 grams, which expression
represents the amount remaining after 30 years?
A. 100(0.5)^30
B. 100(0.5)^3
C. 100(2)^3
D. 30(0.5)^10
Correct Answer: B
Explanation: Half-life problems utilize an exponential decay model with a base of 0.5. The
exponent represents the number of half-life periods that have passed, calculated as total
time divided by half-life duration. After 30 years, exactly 3 half-life periods of 10 years each
have occurred. Substituting these values into the decay formula yields 100(0.5)^3. This
correctly models the reduction of the substance over the specified timeframe.
8. Which property of logarithms is represented by log(ab) = log(a) + log(b)?
A. Power Property
B. Quotient Property
C. Identity Property
D. Product Property
Correct Answer: D
Explanation: The Product Property of logarithms states that the log of a product is equal to
the sum of the logs of its factors. This is a fundamental rule used to expand or condense
logarithmic expressions. In the expression log(ab), ‘a’ and ‘b’ are being multiplied, which is
a product. By applying this property, the expression is rewritten as the sum log(a) + log(b).
Understanding these properties is essential for solving complex algebraic equations
involving logs.
9. Solve for x: sqrt(x - 4) + 2 = 6.
A. x = 8
B. x = 20
C. x = 12
