Q: A chemical reaction is modeled by $$C(t) = 100 - 20\log_{10}(t+1)$$, where $$C is $$the concentration in mg/L and $$t is $$time in hours. What is the concentration after 9 hours?

$$C(9) = 100 - 20\log_{10}(10) = 100 - 20 \times 1 = 80$$

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 $$x \to -\infty$$, $$f(x) \to -\infty$$

Question 1

Which of the following is the correct definition of a rational function?

Accepted Answer

A function that can be written as $$f(x) = \frac{P(x)}{Q(x)}$$ where $$P(x)$$ and $$Q(x)$$ are polynomials and $$Q(x) 
eq 0.$$

Question 2

A business models its revenue with the function $$R(x) = 50x - 0.5x^2$, where x$ is the number of units sold. What number of units maximizes the revenue?

Accepted Answer

$$x = 25$$

Question 3

Which of the following is the correct solution to the equation $$2^x = 32$$?

Accepted Answer

$$x = 5$$

Question 4

A population of bacteria grows according to the exponential model $$P(t) = 200e$$^{0.3t}$$, where t$ is in hours. What is the population after 5 hours?

Accepted Answer

$$P(5) = 200e$$^{1.5}$$ \approx 896$$

Question 5

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

Accepted Answer

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

Question 6

A chemical reaction is modeled by $$C(t) = 100 - 20\log_{10}(t+1)$$, where $$C is $$the concentration in mg/L and $$t is $$time in hours. What is the concentration after 9 hours?

Accepted Answer

$$C(9) = 100 - 20\log_{10}(10) = 100 - 20 	imes 1 = 80$$

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 piecewise function is defined as $$f(x) = \begin{cases} x^2$ & x \u003c 0 \ 2x + 1 & x \geq 0 \end{cases}. $$What is $$f(-3) + f(2)$$?

Accepted Answer

$$f(-3) + f(2) = 9 + 5 = 14$$

Question 9

Which of the following is the correct solution to the equation $$\log_2$(x) = 3$$?

Accepted Answer

$$x = 2^3$ = 8$$

Question 10

A company’s profit is modeled by $$P(x) = -x^2$ + 10x - 16$$, where $$x is $$the number of items produced. What is the maximum profit, and at what value of $$x$$ does it occur?

Accepted Answer

Maximum profit is $$P(5) = 9 at$$ $$x = 5$$

Question 11

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

All real numbers except $$x = 3$$

Question 12

A radioactive substance decays according to $$A(t) = 500e$$^{-0.2t}$$, where A$ is the amount in grams and t$ is time in years. How much remains after 10 years?

Accepted Answer

$$A(10) = 500e$$^{-2}$$ \approx 67.7$$ grams

Question 13

Which of the following is the correct solution to the quadratic equation $$x^2 - 6x + 9 = 0$?

Accepted Answer

$$x = 3$$

Question 14

A car rental company charges $$C(x) = 40 + 0.25x$$ dollars for $$x$$ miles driven. If a customer is charged $$90$$, how many miles did they drive?

Accepted Answer

$$x = 200$$

Question 15

Which of the following is the correct range for the function $$f(x) = e^x$$?

Accepted Answer

$$(0, \infty)$$

Question 16

A student invests $$1000$$ dollars in an account with an annual interest rate of $$5\%$$, compounded continuously. What is the value after $$3$$ years?

Accepted Answer

$$1000e^{0.15}$$ \approx 1162$$

Question 17

Which of the following is the correct solution to the equation $$\log_{10}(x) = 2$$?

Accepted Answer

$$x = 100$$

Question 18

A quadratic function $$f(x) = ax^2$ + bx + c$$ opens upward and has its vertex at $$(2, -3). $$Which of the following statements must be true?

Accepted Answer

$$a \u003e 0$$ and the minimum value is $$-3 at$$ $$x = 2$$

Question 19

A pharmaceutical company models the concentration of a drug in the bloodstream as $$C(t) = 80e$$^{-0.1t}$$, where t$ is in hours. How long will it take for the concentration to drop to 40$ mg/L?

Accepted Answer

$$t = \ln(2) / 0.1 \approx 6.93$$ hours

Math 1111 College Algebra Syllabus and Course Structure

Guida di studio - Domande di pratica

Study guide - Flashcard