Q: A car's value $V$ depreciates exponentially according to $V(t) = 20000 \cdot (0.85)^t$, where $t$ is the number of years after purchase. What is the value after 3 years?

$V(3) = 20000 \cdot (0.85)^3 \approx 12251$

Question 1

Which of the following is the correct solution to the inequality $2x - 5 > 9$?

Accepted Answer

$x > 7$

Question 2

A chemical reaction requires the temperature $T$ (in degrees Celsius) to satisfy $T^2 - 4T - 5 < 0$. What is the range of acceptable temperatures?

Accepted Answer

$-1 < T < 5$

Question 3

Which of the following is the inverse function of $f(x) = 3x + 2$?

Accepted Answer

$f^{-1}(x) = \frac{x - 2}{3}$

Question 4

A population of bacteria doubles every hour. If the initial population is $P_0$, which function models the population after $t$ hours?

Accepted Answer

$P(t) = P_0 \cdot 2^t$

Question 5

Solve for $x$: $\log_{2}(x) = 5$

Accepted Answer

$x = 32$

Question 6

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

Accepted Answer

$x = 3$

Question 7

A pharmaceutical company models the concentration $C$ of a drug in the bloodstream by $C(t) = 50e^{-0.2t}$, where $t$ is in hours. What is the concentration after 5 hours?

Accepted Answer

$C(5) = 50e^{-1} \approx 18.4$

Question 8

Which of the following is the correct factorization of $x^2 - 5x + 6$?

Accepted Answer

$(x - 2)(x - 3)$

Question 9

A car's value $V$ depreciates exponentially according to $V(t) = 20000 \cdot (0.85)^t$, where $t$ is the number of years after purchase. What is the value after 3 years?

Accepted Answer

$V(3) = 20000 \cdot (0.85)^3 \approx 12251$

Question 10

Which of the following is the correct solution to the system of equations: $\begin{cases} x + y = 7 \ x - y = 3 \end{cases}$?

Accepted Answer

$x = 5, y = 2$

Question 11

Which of the following is the correct domain of the function $f(x) = \frac{1}{x-4}$?

Accepted Answer

$x 
eq 4$

Question 12

A medical test result is modeled by the function $f(x) = x^2 - 8x + 15$. For which value of $x$ does the result reach its minimum?

Accepted Answer

$x = 4$

Question 13

Which of the following is the correct solution to $|3x - 7| = 5$?

Accepted Answer

$x = 4$ or $x = \frac{2}{3}$

Question 14

Which of the following is the correct solution to the rational equation $\frac{x}{x-2} = 3$?

Accepted Answer

$x = 6$

Question 15

A company’s profit $P$ is modeled by $P(x) = -2x^2 + 8x - 6$, where $x$ is the number of units sold. What is the maximum profit?

Accepted Answer

$P_{max} = 2$

Question 16

Which of the following is the correct solution to the exponential equation $5^{x} = 125$?

Accepted Answer

$x = 3$

Question 17

A circle has the equation $x^2 + y^2 = 49$. What is the radius of the circle?

Accepted Answer

$7$

Question 18

Which of the following is the correct solution to the polynomial equation $x^3 - 8 = 0$?

Accepted Answer

$x = 2$

Question 19

A radioactive substance decays according to $A(t) = 100e^{-0.3t}$. How long will it take for the substance to decay to $50$ units?

Accepted Answer

$t \approx 2.31$

Question 20

Which of the following is the correct solution to the equation $\sqrt{x + 9} = 5$?

Accepted Answer

$x = 16$

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