Q: Suppose you invest $$15,000 in an index fund at 9% annual interest, compounded monthly, for 30 years. Which formula gives the correct amount A$ after 30 years?

$$A = 15000(1 + \frac{0.09}{12}$$)^{12 \times 30}$$

Q: Which of the following best describes the end behavior of $$f(x) = 2x(3x-1)^2$(x+6)^3(-x+5$$)$?

As $$x \to \infty$$, $$f(x) \to \infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Q: Suppose you invest $$15,000 at 9% annual interest, compounded continuously, for 30 years. What is the correct formula for the amount A$ after 30 years?

$$A = 15000e$$^{0.09 \times 30}$$

Question 1

Which of the following is the correct solution to the quadratic equation $$x^2 - 20x = -99$ using the quadratic formula?

Accepted Answer

$$x = 10 \pm 11$$

Question 2

Given the quadratic function $$f(x) = x^2$ + 6x - 2$$, what is the vertex of the parabola?

Accepted Answer

$$(-3, -11)$$

Question 3

For the function $$f(x) = 2x(3x-1)^2$(x+6)^3(-x+5$$)$, which zero has the graph crossing the x-axis with a flattening effect (i.e., the graph flattens as it crosses)?

Accepted Answer

$$x = -6$$

Question 4

What is the degree and leading term of the polynomial $$f(x) = 2x(3x-1)^2$(x+6)^3(-x+5$$)$?

Accepted Answer

Degree: 7, Leading term: $$2x^7$$

Question 5

If $$f(x) = 3 - x^2$ and g(x) = 2x + 1$, what is f(g(3$$))$$?

Accepted Answer

$$-32$$

Question 6

Given $$f(x) = x^3$ + 1$$ and $$g(x) = \sqrt[3]{x-1}$$, which of the following statements is true?

Accepted Answer

$$f(g(x)) = x$$

Question 7

Suppose you invest $$15,000 in an index fund at 9% annual interest, compounded monthly, for 30 years. Which formula gives the correct amount A$ after 30 years?

Accepted Answer

$$A = 15000(1 + \frac{0.09}{12}$$)^{12 	imes 30}$$

Question 8

Solve for $$x$$: $$3 = \log_x 125$$

Accepted Answer

$$x = 5$$

Question 9

Convert the exponential equation $$64 = 4^x to $$its equivalent logarithmic form.

Accepted Answer

$$x = \log_4$ 64$$

Question 10

Express $$\log \left( \frac{1000x^3$y^4$$}{$$wz^2$$} \right)$ as a sum and/or difference of logarithms with no exponents.

Accepted Answer

$$3\log x + 4\log y + \log 1000 - \log w - 2\log z$$

Question 11

Solve for $$t$$: $$e^{3t} = 9$

Accepted Answer

$$t = \frac{1}{3}\ln 9$$

Question 12

Solve for $$x$$: $$2^{x-2} = 16x$

Accepted Answer

$$x = 6$$

Question 13

Which of the following is the correct solution to $$2\ln(\sqrt{x}) - \ln(6x-1) = 0$$?

Accepted Answer

Question 14

Which of the following best describes the end behavior of $$f(x) = 2x(3x-1)^2$(x+6)^3(-x+5$$)$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o \infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 15

If $$f(x) = x^2$ - 144$$, which of the following is a correct factorization?

Accepted Answer

$$(x - 12)(x + 12)$$

Question 16

Given $$f(x) = x^2$ - 2x + 3$$, what can you say about the real zeros of this function?

Accepted Answer

There are no real zeros.

Question 17

Which of the following is the correct logarithmic form of the equation $$3^{-2}$$ = \frac{1}{9}$$?

Accepted Answer

$$-2 = \log_3$ \frac{1}{9}$$

Question 18

If $$f(x) = x^2$ - 4x + 8$$, what is the axis of symmetry of the parabola?

Accepted Answer

$$x = 2$$

Question 19

Suppose you invest $$15,000 at 9% annual interest, compounded continuously, for 30 years. What is the correct formula for the amount A$ after 30 years?

Accepted Answer

$$A = 15000e$$^{0.09 	imes 30}$$

College Algebra Final Exam Review: Step-by-Step Guidance

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