Practice Test 45 - Algebra 1

20 questions. Answer them in any order, then submit to see your score and every explanation.

The value of a collectible is recorded each month: Month $t$ : 0, 1, 2, 3 Value ($): 200, 230, 264.5, 304.175 From the data, determine if there is constant percent change. If so, what is the percent rate per month?
A car's value depreciates according to $V(t) = 28000(0.85)^t$ , where $t$ is years after purchase. The owner plans to sell the car when its value drops to exactly half the original price. In this context, what information would you need to determine when this occurs, and what role does 0.85 play in that calculation?
Which statements are always true? Choose the option that correctly identifies the always-true statements. I. rational $+$ rational is rational II. irrational $+$ irrational is irrational III. nonzero rational $\times$ irrational is irrational
Given $p(x)=x^2-5$ , what does $p(-3)$ equal?
A company's profit (in thousands of dollars) from selling $x$ hundred items is modeled by $P(x)=-x^2+6x-5$ . On what interval is the profit function increasing?
A bike rental shop charges $12 to rent a bike plus $4 per hour. Let $h$ be the number of hours and let $C$ be the total cost (in dollars). Which equation models this situation?
What is the explicit formula for the arithmetic sequence with $a_1=2$ and common difference $d=-4$ ?
A wildlife population is recorded as follows: Year $t$ : 0, 1, 2, 3 Population: 500, 450, 405, 364.5 From the table, what is the percent change per year, and is it growth or decay?
A population is modeled by $P(t)=P_0(1.10)^t$ where $t$ is in years. Which expression is equivalent and shows an approximate monthly multiplier (use $\approx$ if estimating) for $t$ years?
Which set represents the domain of $f(x)=\dfrac{x+1}{x^2-9}$ ? Give your answer in interval notation.
A taxi charges a flat fee of $4 plus $2 per mile. Does this situation involve a constant rate of change (change in cost per change in miles)?
A company's profit function is modeled by $P(x) = \begin{cases} -x^2 + 8x & \text{if } 0 \leq x \leq 4 \\ \sqrt{x + 12} + 12 & \text{if } x > 4 \end{cases}$ where $x$ represents months since January and $P(x)$ represents profit in thousands of dollars. What is the profit in May ( $x = 4$ ) minus the profit in July ( $x = 6$ )?
Is the expression $3\sqrt{7}$ rational or irrational? Choose the option with correct reasoning.
A car worth $\$20{,}000$ depreciates by 15% each year. Which describes the change in the car's value over time?
The function $g(x)=\sqrt{x-2}$ is used to model the length (in centimeters) of a piece cut from a strip, where $x$ is a measurement in centimeters. What is the mathematical domain of $g$ ?
What is the sum of $\left(x^3 - 2x^2 + x - 8\right)$ and $\left(2x^3 + x^2 - 5x + 3\right)$ ?
Use completing the square to find the solutions to $x^2 - 4x + 1 = 0$ .
Which method is most efficient for solving $x^2 - 49 = 0$ ?
A polynomial is given by $P(x)=(x-2)^3(x+1)$ . Use zeros and multiplicity to decide how the graph behaves at each x-intercept for a rough sketch. Which statement is correct?
The amount of a medicine in the bloodstream is modeled by $M(t) = 200(0.9)^t$ , where $t$ is hours after the dose and $M(t)$ is in milligrams. What does it mean that the base is $0.9$ ?

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