Q: A car's value $$V$$ depreciates exponentially according to $$V(t) = 20000 \times (0.85)^t$$, where $$t is $$the number of years since purchase. What is the value after 5 years?

$$V(5) = 20000 \times (0.85)^5$ \approx 8863$$

Q: A biologist models the growth of a plant with $$h(t) = 2t^2$ + 3t + 1$$, where $$h is $$height in cm and $$t is $$time in weeks. What is the height after 4 weeks?

$$h(4) = 2 \times 16 + 3 \times 4 + 1 = 32 + 12 + 1 = 45 cm$$

Q: A city’s population $$P$$ grows according to $$P(t) = 10000 \times e$$^{0.03t}$$, where t$ is years since 2000. What is the population in 2020?

$$P = 10000 \times e$$^{0.6}$$ \approx 18211$$

Q: Which of the following is the correct solution to $$\sin(\theta) = 0.5$$ for $$0 \leq \theta \u003c 360$$^{\circ}$$?

$$\theta = 30$$^{\circ}$$ and 150$$^{\circ}$$

Question 1

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

Accepted Answer

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

Question 2

A chemical reaction's rate $$R is $$modeled by the function $$R(t) = 5e$$^{-0.2t}$$, where t$ is time in minutes. What is the rate after 10 minutes?

Accepted Answer

$$R(10) = 5e$$^{-2}$$ \approx 0.68$$

Question 3

Which of the following equations represents a line with slope $$m = -3$$ and $$y-$$intercept $$b = 5$$?

Accepted Answer

$$y = -3x + 5$$

Question 4

A hospital tracks the number of patients $$P$$ admitted each day using the quadratic model $$P(d) = -2d^2$ + 20d + 50$$, where $$d is $$the day of the month. On which day is the maximum number of patients admitted?

Accepted Answer

$$d = 10$$

Question 5

Which of the following is the correct solution to the equation $$2x^2 - 8x = 0$?

Accepted Answer

$$x = 0$$ and $$x = 4$$

Question 6

A population of bacteria doubles every 3 hours. If the initial population is $$P_0 = 500$, what is the population after 9 hours?

Accepted Answer

$$P = 500 	imes 2^3$ = 4000$$

Question 7

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

Accepted Answer

$$(x - 3)(x + 3)$$

Question 8

A car's value $$V$$ depreciates exponentially according to $$V(t) = 20000 	imes (0.85)^t$$, where $$t is $$the number of years since purchase. What is the value after 5 years?

Accepted Answer

$$V(5) = 20000 	imes (0.85)^5$ \approx 8863$$

Question 9

Which of the following is the solution set for $$|x - 4| = 7$$?

Accepted Answer

$$x = -3$$ and $$x = 11$$

Question 10

A medication's concentration $$C in $$the bloodstream is modeled by $$C(t) = 100e$$^{-0.5t}$$, where t$ is in hours. How long until the concentration drops to 25$ mg/L?

Accepted Answer

$$t = 2.77$$ hours

Question 11

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

Question 12

A company’s profit $$P is $$given by $$P(x) = -4x^2$ + 40x - 36$$, where $$x is $$the number of units sold. What is the maximum profit?

Accepted Answer

Question 13

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 14

A biologist models the growth of a plant with $$h(t) = 2t^2$ + 3t + 1$$, where $$h is $$height in cm and $$t is $$time in weeks. What is the height after 4 weeks?

Accepted Answer

$$h(4) = 2 	imes 16 + 3 	imes 4 + 1 = 32 + 12 + 1 = 45 cm$$

Question 15

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

Accepted Answer

$$x = 32$$

Question 16

A city’s population $$P$$ grows according to $$P(t) = 10000 	imes e$$^{0.03t}$$, where t$ is years since 2000. What is the population in 2020?

Accepted Answer

$$P = 10000 	imes e$$^{0.6}$$ \approx 18211$$

Question 17

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

Accepted Answer

$$x = -3$$

Question 18

A scientist mixes two solutions: one with 30% salt and one with 10% salt. How many liters of each should be mixed to obtain 20 liters of a 20% salt solution?

Accepted Answer

5 liters of 30% and 15 liters of 10%

Question 19

Which of the following is the correct solution to $$\sin(	heta) = 0.5$$ for $$0 \leq 	heta \u003c 360$$^{\circ}$$?

Accepted Answer

$$	heta = 30$$^{\circ}$$ and 150$$^{\circ}$$

Math 1030 College Algebra Syllabus and Study Guide

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드