WeBWorK : mathprep : Section09SettingUpFunctionsTest : v4

Problem 1.

(1 point)

After $t$ years, the population $P$ of fuzzy-headed newts is given to be $P = M(1 - {M - P_0\over M} e^{-kt})$ , where $M$ is the maximum possible newt population, $P_0$ the initial newt population and $k$ a growth rate. Which of the following is true?

A. $P$ is the name of a function, $M$ and $t$ are variables and $P_0$ and $k$ are constants.
B. $P$ and $M$ are names of functions, $t$ is a variable, and $P_0$ and $k$ are constants.
C. $P$ and $M$ are variables, and $P_0$ , $k$ and $t$ are constants.
D. $P$ and $t$ are variables, and $M$ , $P_0$ and $k$ are constants.
E. None of the other options is true.

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Problem 2.

(1 point)

A refrigerator has a square base that is 4 units on each side. Express its height $h$ as a function of its volume $V$ .
$h(V) =$

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Problem 3.

(1 point)

The cost, $C$ , of manufacturing $p$ units of item~1 and $q$ units of item~2, costing $k_1$ and $k_2$ dollars per unit, respectively, is $C = k_1 p + k_2 q$ . Which of the following is true?

A. $C$ is the name of a function and $p$ , $q$ , $k_1$ and $k_2$ are constants.
B. $C$ is the name of a function, and all of $p$ , $q$ , $k_1$ and $k_2$ are variables.
C. $C$ , $p$ , $q$ , $k_1$ and $k_2$ are all variables.
D. $C$ , $p$ and $q$ are variables, and $k_1$ and $k_2$ are constants.
E. None of the other options is true.

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Problem 4.

(1 point)

If $B = 2 p + q$ and $q - 2p = 1$ , write a formula for the function $B(p)$ .
$B(p) =$

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Problem 5.

(1 point)

A cylindrical water tank drains through a hole in its bottom. The water level $y$ in the tank after $t$ seconds is $y = (\sqrt{y_0} - \alpha \sqrt{2g}t)^2$ , where $y_0$ is the initial water-level, $\alpha$ a measure of the size of the hole, and $g$ the acceleration due to gravity. Which of the following is true?

A. $y$ , $t$ and $\alpha$ represent variables, and $y_0$ and $g$ are constants.
B. $y$ is the name of a function, $t$ and $\alpha$ represent variables, and $y_0$ and $g$ are constants.
C. $y$ and $t$ represent variables and $y_0$ , $\alpha$ and $g$ are constants.
D. $y$ is the name of a function, $\alpha$ represents a variable, and $t$ , $y_0$ and $g$ are constants.
E. $y$ , $t$ and $y_0$ represent variables, and $\alpha$ and $g$ are constants.

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