Practice Test 4 - College Algebra

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

If $2x^2 + kx + 18$ can be factored as $(2x + a)(x + b)$ where $a$ and $b$ are integers, what is the value of $k$ ?
How can the change of base formula be used to rewrite $\log_3(81)$ in terms of natural logarithms?
The function $g(x) = \frac{ax^3 + bx^2 + cx + d}{x^2 - 4}$ has a slant asymptote with equation $y = 3x + 2$ . If the function has a vertical asymptote at $x = 2$ but not at $x = -2$ , what must be true about the coefficients?
Simplify $\frac{x^3-8}{x^2+2x+4} \div \frac{x^2-4}{x^2+4x+4}$ .
If $\log_b(x)=m$ and $\log_b(y)=n$ , what is $\log_b\!\left(\frac{x}{y}\right)$ ?
A ball is thrown upward from the top of a 96-foot building with an initial velocity of 80 feet per second. The height $h$ (in feet) is given by $h(t) = -16t^2 + 80t + 96$ . How long does it take for the ball to reach its maximum height, and when does it hit the ground?
A student wants to evaluate $\log_{0.5}(8)$ using a calculator that only has base-10 logarithms. After applying the change of base formula correctly, which numerical calculation should be performed?
Which of the following correctly applies the product rule to $\log_b(7x)$ ?
A polynomial function $f(x)$ of degree 7 has the property that $f'(x) = 0$ has exactly 4 real solutions. If $f(x)$ has leading coefficient 3, which statement best describes the behavior and characteristics of $f(x)$ ?
Recipe: solve $\frac{x}{2}+\frac{1}{3}=\frac{5}{6}$ for $x$ cups.
How can $\log_b\!\left((x^2)^5\right)$ be rewritten using the power rule?
A student claims that $f(x) = \frac{x^4 + 2x^3 - 5x^2 + 1}{3x^4 - x^3 + 7x - 2}$ has a horizontal asymptote at $y = \frac{1}{3}$ because both the numerator and denominator have degree 4, so the horizontal asymptote equals the ratio of leading coefficients. Which analysis of this claim is correct?
Budgeting: Solve $7x-14<21$ for weekly transport cost; express solution in interval notation.
If $\log_a(x) = 3.2$ and $\log_b(x) = 4.8$ , what is the value of $\log_a(b)$ expressed in terms of these given values?
Cost sharing: solve $\frac{x}{6}+\frac{1}{12}=\frac{5}{12}$ dollars for $x$ .
The rational function $p(x) = \frac{-2x^5 + 3x^3 + x}{4x^5 - x^4 + 7x^2 - 3}$ has end behavior that can be described as approaching which horizontal asymptote?
A retirement account currently has $85,000$ and earns $6.3\%$ annual interest compounded quarterly. If no additional contributions are made, what will be the account balance when it reaches $200,000$ ?
A bacteria culture starts with 500 bacteria and doubles every 3 hours. At the same time, due to environmental factors, 50 bacteria die every hour regardless of the population size. Which equation best models the bacteria population $P$ after $t$ hours?
Which option correctly simplifies $\log_b\!\left(\frac{5x}{y}\right)$ ?
Budgeting: Solve $12\le 3x+6$ for minimum deposit; express solution in interval notation.

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