Practice Test 95 - Algebra 2

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

A town's population is modeled by $P(t)=18{,}000(1.02)^t$ , where $t$ is measured in years and $P(t)$ is the number of people. In this function, what does it mean that the base is $1.02$ ?
What is the y-intercept of the exponential function $f(x)=-4\cdot 3^x$ ?
A quadratic with real coefficients has the form $ax^2+bx+c=0$ . In the complex numbers, it always has exactly 2 solutions counting multiplicity, and if it has a nonreal complex solution then the solutions occur in conjugate pairs. If $2+3i$ is a solution of a quadratic with real coefficients, what must the other solution be (so that there are exactly 2 complex solutions counting multiplicity)?
When $(3x - 2y)^4$ is expanded using the Binomial Theorem, what is the coefficient of the $x^2y^2$ term?
A polynomial $f(x)$ has the property that $f(-3) = 8$ and $f(1) = 0$ . When $f(x)$ is divided by $x^2 + 2x - 3$ , what is the remainder?
The matrix equation $\begin{bmatrix}1&0&-2\\0&3&1\\4&-1&0\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}6\\-5\\8\end{bmatrix}$ represents which system of equations?
Use a calculator to solve the exponential equation $2.5\cdot 10^{0.3t}=18$ for $t$ . Write the exact solution using common logarithms ( $\log$ ) and then approximate.
A ball is tossed upward from a platform. Its height in meters after $t$ seconds is modeled by $h(t)=-5t^2+20t+2$ . Graph the equation for $0\le t\le 5$ with appropriate labels and a reasonable scale.
The equation $x^2 + 6x + k = 0$ is completed to the square form $(x + 3)^2 = m$ . If this equation has exactly one solution, what is the relationship between $k$ and $m$ ?
See structure within complexity by identifying an independent part: $f(x,k)=k\,(x^2-4x+7).$ Which statement correctly interprets the expression by viewing $(x^2-4x+7)$ as a single entity and describing what changing $k$ does?
For $g(x)=x^2(x-5)^3,$ identify the zeros and their multiplicities, describe how the graph behaves at each zero (crosses or touches, and whether it flattens), and state the end behavior.
A contractor can paint a house in 12 hours. A second contractor can paint the same house in 18 hours. Write and solve an equation to find how long it takes them to paint the house working together. Let $t$ = the time (in hours) for both contractors working together.
Use technology to find $A^{-1}$ and solve the system using $X=A^{-1}B$ . $\begin{cases} 2x+y+z=9 \\ x-y+z=5 \\ 3x+y-z=3 \end{cases}$ Which solution vector $X=\begin{bmatrix} x \\ y \\ z \end{bmatrix}$ is correct?
The graph of $f(x)=x^2$ is shown. The graph of $g(x)$ has the same shape and vertex at $(0,-2)$ . Which equation matches $g(x)$ ?
Let $f(x)=x^3-x$ . Show using symmetry rules whether $f$ is even, odd, or neither by considering $f(-x)$ relative to $f(x)$ .
A moving company models the cost (in dollars) to rent a truck for $h$ hours by $C(h)=\dfrac{120}{10-h}$ . In the real situation, $h$ is the number of hours the truck is rented, and the company allows rentals for up to 9 hours. What is an appropriate realistic domain for $h$ ?
The graph shows function $h(x)$ , a cubic polynomial. Function $j(x) = x^3 - 6x^2 + 9x + 2$ . Compare the number of relative extrema (local maxima and minima combined) for these two functions.
Find all solutions in the complex numbers of $x^2-4x+5=0$ . Recall: every quadratic $ax^2+bx+c=0$ has exactly 2 complex solutions counting multiplicity (2 distinct real, 1 repeated real, or 2 complex conjugates), and the discriminant $b^2-4ac$ determines the type.
The value of a used laptop is modeled by $V(t)=900(0.80)^t$ , where $V$ is the value in dollars and $t$ is time in years since purchase. In the function, interpret the base $0.80$ .
A quantity decays by 10% per year, modeled by $(0.90)^t$ after $t$ years. Rewrite $(0.90)^t$ to show an equivalent monthly decay factor applied over $12t$ months. Which rewrite is correct?

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