Practice Test 30 - Algebra 2

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

Solve $2^x=3x+1$ using a table of values (successive approximations). Use the values below to choose the best approximation for the solution, to the nearest tenth. Table: - At $x=2.0$ : $2^x=4.0$ and $3x+1=7.0$ - At $x=2.5$ : $2^x\approx 5.7$ and $3x+1=8.5$ - At $x=2.8$ : $2^x\approx 7.0$ and $3x+1=9.4$ - At $x=3.0$ : $2^x=8.0$ and $3x+1=10.0$ - At $x=3.2$ : $2^x\approx 9.2$ and $3x+1=10.6$ - At $x=3.4$ : $2^x\approx 10.6$ and $3x+1=11.2$ - At $x=3.5$ : $2^x\approx 11.3$ and $3x+1=11.5$ - At $x=3.6$ : $2^x\approx 12.1$ and $3x+1=11.8$
A bacteria culture grows according to $N(t)=500(1.20)^t$ , where $N$ is the number of bacteria and $t$ is time in hours. What is the growth rate as a percent per hour?
Determine whether the system has one solution, no solution, or infinitely many solutions: $\begin{cases} 2x - 4y = 10 \\ x - 2y = 5 \end{cases}$
What is $t$ in the equation $7\cdot 10^{t/3}=50$ ? Express $t$ as a logarithm and evaluate using technology.
Which statement best compares the effects of $f(2x)$ and $2f(x)$ on the graph of a general function $f$ ?
On the complex plane, the distance between $z_1=a+bi$ and $z_2=c+di$ is the modulus of their difference: $|z_1-z_2|=\sqrt{(a-c)^2+(b-d)^2}$ . What is the distance between $z_1=-2-i$ and $z_2=3+2i$ ?
A factory's daily production cost is $C(n) = 0.5n^2 + 100n + 2000$ dollars for $n$ units. The factory operates only on weekdays and has a maximum daily capacity of 150 units. Which domain best represents this situation?
A theme park models the number of visitors (in hundreds) $V(t)$ at time $t$ hours after opening as a periodic function. The pattern repeats every 6 hours, and $V(1)=8$ . What is $V(13)$ ?
Which restriction(s) make $f(x)=x^2$ pass the horizontal line test? (Choose one option.)
A savings account balance is modeled by $B(t)=500(1.04)^t$ , where $t$ is the number of years since the account was opened and $B(t)$ is in dollars. In this function, what does the parameter $500$ represent in context?
Order the following functions by eventual growth rate (from slowest to fastest) as $x\to\infty$ : $\ell(x)=3x+7$ (linear), $q(x)=x^2$ (quadratic), $p(x)=x^5$ (polynomial), $e(x)=1.2^x$ (exponential).
The complex number $z = 3 - 4i$ is represented as a point on the complex plane. When $z$ is multiplied by $i$ , the resulting point is obtained by which geometric transformation of the original point?
Use logarithms to solve the equation $2.5\cdot e^{t/4}=40$ for $t$ . Give the exact solution and an approximate value using a calculator.
Use the Rational Zeros Theorem to list all possible rational zeros of $P(x)=3x^3-2x^2+x-6.$ (Remember: any rational zero $\frac{p}{q}$ in lowest terms has $p\mid$ constant term and $q\mid$ leading coefficient.)
Subtract and simplify to lowest terms. (The difference of rational expressions is still a rational expression.) Subtract: $\dfrac{x+1}{x^2-4}-\dfrac{3}{x-2}$ (assume denominators are nonzero).
A student graphs $y=f(x)$ and $y=g(x)$ and sees they intersect at the point $(4,7)$ . Which equation must be true?
Addition of complex numbers corresponds to vector addition on the complex plane. If $z_1=1+2i$ and $z_2=4-3i$ , what point represents $z_1+z_2$ ?
Determine whether the relationship is linear or exponential, then write the function. $x$ : 1, 2, 3, 4 $y$ : 2, 6, 18, 54
A bacteria culture is modeled by $N(t)=N_0\cdot 2^{3t}.$ If you view $2^{3t}$ as a single entity (a growth factor), which interpretation is correct about what depends on $N_0$ ?
Demonstrate that the polynomial identity $(x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2$ holds for all real $x,y$ by expanding both sides and simplifying.

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