Deck 13: A Quantitative Approach to Algebra and Graphing

Question 1

Reason quantitatively to complete the following sentences.

A) As the demand for housing increases, the price of housing _____.
B) Say that

describes the relationship between the Celsius temperature C of a liquid and the time t in hours. Then "- 20t" tells you that _____.

Answer 1

A) increases
B) the temperature goes down 20 Celsius degrees each hour.

Question 2

Complete each sentence with "increases," "decreases," "doesn't change," or "can't say anything definite," as appropriate.

A) As the semester goes on, the number of days until final exams _____.
B) As a person's peanut butter consumption increases, her miles traveled to work _____.
C) As the speed of a car increases, the stopping distance of the car _____.
D) As the number of calculations increases, the probability of an error _____.

Answer 2

A) decreases B) doesn't change C) increases D) increases

Question 3

What coordinate graphing conventions are being violated by the following graph of data showing candy bar sales for three children who sold for different amounts of time?

Answer 3

Mainly, the scale on the hours-spent axis is not consistent. The fact that the scale on the vertical axis does not start at zero is sometimes done, so that is less serious.

Question 4

Below is a graph for candle 1. Candle 2 (graph not given) burns according to $h ={}^{ -} 2 t + 25$
, where h is the height of the candle in cm t minutes after being lit.

A) Which candle, 1 or 2, burns at a faster rate? Explain.
B) Write an equation that describes candle 1's height h versus time burning t.
$h =$$\underline{\quad\quad}$
C) On the above coordinate system, draw the graph for the burning of candle 2: ( $h ={}^{-} 2 t + 25$ ). What information does the 25 give?
D)Exactly how many minutes will candle 2 last after it is lit?
E)If the two candles, 1and 2, are lit at the same time, will they ever be the same height (before they both burn out)? If yes, tell when (approximately). If no, tell why not.

Question 5

The bowling place is under new ownership! The new owners plan to charge for shoes and ball rental, and of course for each game, so that their dollar income I from a bowler who rents shoes and a ball and who bowls n games is I = 2n + 2.5.

A) How much are they planning to charge for shoes and ball rental?
B) That plan did not work, so they want to try a new plan (graph below). How much will they charge per game under the new plan?

C) Will they make more money under the new plan? Explain.

Question 6

A bakery keeps records and makes graphs of its cookie production. Below are partial graphs for two days.

A) Write a story that might tell what happened on Tuesday. Do not introduce any numbers besides those indicated for Tuesday.

B) What is the slope for Friday's graph, and what does that slope mean about the cookie situation? Show your work.

Question 7

A new candle is 12 inches long and burns 3 inches every 20 minutes. In a graph showing the height (in inches) of the candle as it burns minute by minute, what is the slope? What does that slope mean in this situation?

Question 8

Put the letter of the line in the graph below with the equation with which it would MOST likely to belong.
___ y = 2x + 7
___ y = - 2x + 7
___ y = x
___ y =
x

Question 9

Write an equation for each of these, and also a story for the graph in part B. You may or may not use the whole line, depending on your story.

A) Our dog eats
pound of dog food every day. We buy a bag that weighs 24 pounds. What amount A remains after d days?

Question 10

The Hiker's Supply Company's Snack Mix Recipe
Ingredients: 3 cups of nuts
1 cup of raisins
2 cups of M&Ms
Combine and mix well. Yields: 9 packages of snack mix.

A) How many cups of ingredients are in one package of snack mix? Explain.
B) What fractional part of each package of snack mix is M&Ms?
C) What fractional part of two packages of snack mix is M&Ms?
D) How many cups of M&Ms are in two packages of trail mix? Explain.
E) If you need 24 packages of snack mix, what quantities of nuts, raisins, and M&Ms do you need? (No explanation is required, but show your work.)

Question 11

A machine for producing choco-nuts gives 5 choco-nut hearts for every 4 chocolate bars and $\frac { 1 } { 2 }$
a cup of nuts put into the machine (nothing is lost in the machine).
Solve by reasoning. Your reasoning may involve calculations, but not by just calculating with a proportion.

A) How many hearts (partial or otherwise) would the machine give for 18 bars and the right amount of nuts?
B) How many cups of nuts would be the right amount for 18 bars?
C) An order for 48 hearts comes in. How many bars will that order take?

Question 12

Do the following describe linear or nonlinear relationships? Explain.

A) Plant's height

B) Dripping water

Question 13

The following table describes a linear relationship.

A) Complete the table.
$\begin{array} { | l | l | } \hline x & y \\\hline - 8 & - 21 \\\hline - 7 & - 19 \\\hline - 3 & \\\hline & - 5 \\\hline 3 & \\\hline\end{array}$
B) Is this relationship proportional?

Question 14

The following table describes a linear relationship. Complete the table and write the rule. $\begin{array} { | l | l | } \hline x & y \\\hline 2 & 6 \\\hline 5 & \\\hline 7 & 8.5 \\\hline & 9.5 \\\hline 10 & 10 \\\hline\end{array}$

Question 15

In science class, students measured the height of a bouncing ball. Each bounce was half as high as the one before it. What type of function describes the sequence of bounce heights?

A) linear
B) absolute value
C) quadratic
D) exponential

Question 16

The street newspaper vendor gets $0.25 for each $1.25 newspaper he sells. Write an algebraic equation describing the relationship between the number of papers sold and the amount the vendor earns. Does the equation describe a linear or nonlinear function? Explain.

Question 17

There are initially two rabbits. Each month, the number of rabbits is twice the number of the month before. Write an algebraic equation describing the relationship between the number of months x and the number of rabbits y. Does the equation describe a linear or nonlinear function? Explain.

Question 18

Are the following functions linear or nonlinear? Explain.

A) ${}^{-} \frac { 1 } { 4 } x + 3 y = 0$
B) y = x(x-2)
C) y = |-2|x
D) A = $\pi$ r²