Q: A car depreciates in value by $$15\%$$ each year. If the car is currently worth $$\20$$,000$$, what will its value be after 3$ years?

$$20,000 \times (0.85)^3$ \approx \12$$,281$

Question 1

Which of the following best describes the process of synthesizing results from the graphs and equations of functions?

Accepted Answer

Comparing the graphical and algebraic representations to draw conclusions about the function's behavior.

Question 2

A biologist models the population of a bacteria culture with the function $$P(t) = 500e$$^{0.3t}$$, where t$ is time in hours. What is the approximate population after 5 hours?

Accepted Answer

$$P(5) = 500e$$^{1.5}$$ \approx 2241$$

Question 3

Which of the following equations represents a linear equation?

Accepted Answer

$$2x + 3y = 7$$

Question 4

A company’s profit $$P (in $$dollars) from selling $$x$$ units is modeled by $$P(x) = -2x^2$ + 400x - 1000. $$What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$39,000 at$$ $$x = 100$$ units.

Question 5

Which of the following is the solution set for the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

$$-1 \u003c x \u003c 6$$

Question 6

A chemist needs to mix a $$30\%$$ saline solution with a $$10\%$$ saline solution to obtain $$20$$ liters of a $$20\%$$ solution. How many liters of the $$30\%$$ solution should be used?

Accepted Answer

$$10$$ liters

Question 7

Which of the following is the correct solution to the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2,\ y = 3$$

Question 8

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x - 4)(x - 5)$$

Question 9

A radioactive substance decays according to $$A(t) = 1000e$$^{-0.2t}$$, where t$ is in years. After how many years will only 100$ grams remain?

Accepted Answer

$$t = \frac{\ln(0.1)}{-0.2} \approx 11.5$$ years

Question 10

Which of the following is the correct solution to the equation $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 11

Which of the following describes the graph of $$y = |x - 3| + 2$$?

Accepted Answer

A V-shaped graph with vertex at $$(3, 2)$$

Question 12

A quadratic equation $$ax^2 + bx + c = 0$ has real and distinct solutions if:

Accepted Answer

$$b^2 - 4ac$$ \u003e 0$$

Question 13

Which of the following is the sum of the first $$5$$ terms of the arithmetic sequence where $$a_1 = 3$ and d = 4$?

Accepted Answer

$$S_5 = 3 + 7 + 11 + 15 + 19 = 55$

Question 14

Which of the following is the equation of a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 15

A car depreciates in value by $$15\%$$ each year. If the car is currently worth $$\20$$,000$$, what will its value be after 3$ years?

Accepted Answer

$$20,000 	imes (0.85)^3$ \approx \12$$,281$

Question 16

Which of the following is the correct solution to the rational equation $$\frac{2}{x} + 1 = 3$$?

Accepted Answer

$$x = 1$$

Question 17

Which of the following is the inverse function of $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{3}$$

Question 18

A system of inequalities is given by $$\begin{cases} y \u003e 2x + 1 \ y \u003c -x + 4 \end{cases}. $$Which of the following points is in the solution set?

Accepted Answer

$$(1, 4)$$

Question 19

Which of the following is the sum of the infinite geometric series $$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots$$?

Accepted Answer

$$2$$

Intermediate Algebra Course Syllabus and Success Guide – Math C110

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