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Mar 23, 2024
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A certain college had 3,000 students enrolled in 2015. The college predicts that after 2015, the number of students enrolled each year will be 2% less than the number of students enrolled the year before. Which of the following functions models the relationship between the number of students enrolled, $f(x)$, and the number of years after 2015, $x$ ?
Difficulty: Medium
A:

$f(x)=0.02(3,000)^{x}$

B:

$f(x)=0.98(3,000)^{x}$

C:

$f(x)=3,000(0.02)^{x}$

D:

$f(x)=3,000(0.98)$

The function $f(x)=200,000(1.21)^{x}$ gives a company's predicted annual revenue, in dollars, $x$ years after the company started selling light bulbs online, where $0<$x$\leq 10$. What is the best interpretation of the statement "$f(5)$ is approximately equal to 518,748" in this context?
Difficulty: Easy
A:

5 years after the company started selling light bulbs online, its predicted annual revenue is approximately 518,748 dollars.

B:

5 years after the company started selling light bulbs online, its predicted annual revenue will have increased by a total of approximately 518,748 dollars.

C:

When the company's predicted annual revenue is approximately 518,748 dollars, it is 5 times the predicted annual revenue for the previous year.

D:

When the company's predicted annual revenue is approximately 518,748 dollars, it is 5% greater than the predicted annual revenue for the previous year.

The given equations define the functions $f$ and $g$, where $x\geq 0$. Which of the following equations displays, as a constant or coefficient, the maximum value of the function it defines, where $x\geq 0$?

I. $f(x)=33(0.4)^{x+3}$
II. $g(x)=33(0.16)(0.4)^{x-2}$
Difficulty: Hard
A:

I only

B:

II only

C:

I and II

D:

Neither I nor II

Blood volume, $V_{B}$, in a human can be determined using the equation $V_{B}=\dfrac{V_{P}}{1-H}$, where $V_{P}$ is the plasma volume and $H$ is the hematocrit (the fraction of blood volume that is red blood cells). Which of the following correctly expresses the hematocrit in terms of the blood volume and the plasma volume?
Difficulty: Medium
A:

$H=1-\dfrac{V_{P}}{V_{B}}$

B:

$H=\dfrac{V_{B}}{V_{P}}$

C:

\(H=1+\dfrac{V_{B}}{V_{P}}\)

D:

$H=V_{B}-V_{P}$

$P=\frac{W}{t}$
The power $P$ produced by a machine is represented by the equation above, where $W$ is the work performed during an amount of time $t$. Which of the following correctly expresses $W$ in terms of $P$ and $t$?
Difficulty: Easy
A:

$W =Pt$

B:

$W = \frac{P}{t}$

C:

$W = \frac{t}{P}$

D:

$W = P+t$

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