Q: A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

$$P(t) = 500 \times 2$$^{t/3}$$

Q: Which of the following describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

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

Q: A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height reached by the ball?

Maximum at $$t = \frac{-b}{2a} = \frac{-20}{2 \times -4.9} \approx 2.04$$; $$h(2.04) \approx 21.98$$ meters

Question 1

Which of the following is the correct definition of the domain of a function $$f(x)$$?

Accepted Answer

The set of all possible input values $$x$$ for which $$f(x) is $$defined.

Question 2

A pharmaceutical company models the concentration $$C of a $$drug in the bloodstream over time $$t (in $$hours) by the function $$C(t) = 5e$$^{-0.3t}$$. What is the concentration after 4 hours?

Accepted Answer

$$C(4) = 5e$$^{-1.2}$$ \approx 1.51$$

Question 3

Which of the following is the inverse of the function $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{2}$$

Question 4

A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 500 	imes 2$$^{t/3}$$

Question 5

Which of the following is a solution to the quadratic equation $$x^2 - 6x + 8 = 0$?

Accepted Answer

$$x = 2$$

Question 6

A car rental company charges a flat fee of $$\30$ plus $$\$$0.20$$ per mile driven. Which function models the total cost $$C$$ for driving $$m$$ miles?

Accepted Answer

$$C(m) = 30 + 0.20m$$

Question 7

Which of the following describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

Accepted Answer

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

Question 8

A chemical reaction follows the equation $$A(t) = 100 - 20\ln(t+1)$$, where $$A is $$the amount of reactant left after $$t$$ minutes. How much reactant remains after 2 minutes?

Accepted Answer

$$A(2) = 100 - 20\ln(3) \approx 78.03$$

Question 9

Which of the following is the correct solution set for the inequality $$x^2 - 4x$$ \u003c 0$$?

Accepted Answer

$$0 \u003c x \u003c 4$$

Question 10

A medical test result is modeled by the function $$T(x) = \frac{100}{1 + e$$^{-0.5x}$$}$$, where $$x is $$the number of hours after administration. What is $$T(0)$$?

Accepted Answer

$$T(0) = \frac{100}{1 + 1} = 50$$

Question 11

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

$$a_1$$ + $$a_2$$ + $$a_3$$ + $$a_4$$ + $$a_5 = 3 + 7 + 11 + 15 + 19 = 55$

Question 12

A system of equations is given by $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}. $$What is the solution $$(x, y)$$?

Accepted Answer

$$(x, y) = (2, 1)$$

Question 13

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 14

A radioactive substance decays according to $$N(t) = N_0$ e$$^{-kt}$$. If N_0$ = 200$$ and $$k = 0.1$$, what is $$N(10)$$?

Accepted Answer

$$N(10) = 200e$$^{-1}$$ \approx 73.58$$

Question 15

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

Accepted Answer

$$x = 32$$

Question 16

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height reached by the ball?

Accepted Answer

Maximum at $$t = \frac{-b}{2a} = \frac{-20}{2 	imes -4.9} \approx 2.04$$; $$h(2.04) \approx 21.98$$ meters

Question 17

Which of the following is the sum of the infinite geometric series $$\sum_{n=0}^{\infty} 5 \left(\frac{1}{3}\right)^n$$?

Accepted Answer

$$S = \frac{5}{1 - \frac{1}{3}} = \frac{5}{\frac{2}{3}} = 7.5$$

Question 18

A matrix equation is given by $$\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 11 \end{bmatrix}. $$What is the value of $$x$$?

Accepted Answer

$$x = 1$$

Question 19

Which of the following is the correct expression for the sum of the first $$n$$ terms of an arithmetic sequence with first term $$a_1$$ and common difference $$d$$?

Accepted Answer

$$S_n = \frac{n}{2}[2a_1 + (n-1)d]$$

College Algebra (MATH-1314) Course Overview and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard