Question

1. chapter problem a city opened a new landfill site in 2000. the table shows how much garbage was added to the landfill in each year from 2000 to 2007.

year garbage added (1000s of tonnes)
2000 200
2001 230
2002 258
2003 287
2004 317
2005 347
2006 376
2007 406
a) determine the total mass of garbage in the landfill at the end of each year.
b) make a scatter plot of the total mass of garbage versus the year. draw a curve of best fit.
c) what problems do you predict if growth continues at its current rate?

1. a rectangle has a width of x centimetres, and its length is double its width.

a) create a table comparing the length and area of a rectangle for widths up to 8 cm.
b) make a scatter plot of the data.
c) draw a curve of best fit.
d) explain why the graph of this relation is non - linear.

Explanation:

Question 6 - Part a

Step1: Initialiser la somme

La somme initiale en 2000 est égale à la quantité de déchets ajoutée en 2000, soit $S_{2000}=200$.

Step2: Calculer la somme pour chaque année suivante

Pour 2001 : $S_{2001}=S_{2000}+230 = 200 + 230=430$.
Pour 2002 : $S_{2002}=S_{2001}+258 = 430+258 = 688$.
Pour 2003 : $S_{2003}=S_{2002}+287 = 688+287 = 975$.
Pour 2004 : $S_{2004}=S_{2003}+317 = 975+317 = 1292$.
Pour 2005 : $S_{2005}=S_{2004}+347 = 1292+347 = 1639$.
Pour 2006 : $S_{2006}=S_{2005}+376 = 1639+376 = 2015$.
Pour 2007 : $S_{2007}=S_{2006}+406 = 2015+406 = 2421$.

Question 7 - Part a

Step1: Trouver l'expression pour la longueur et l'aire

La longueur $l = 2x$ et l'aire $A=l\times w=2x\times x = 2x^{2}$.

Step2: Créer le tableau

Largeur $x$ (cm)	Longueur $l = 2x$ (cm)	Aire $A = 2x^{2}$ ($cm^{2}$)
2	4	8
3	6	18
4	8	32
5	10	50
6	12	72
7	14	98
8	16	128

Answer:

Question 6 - Part a

$S_{2000}=200$, $S_{2001}=430$, $S_{2002}=688$, $S_{2003}=975$, $S_{2004}=1292$, $S_{2005}=1639$, $S_{2006}=2015$, $S_{2007}=2421$ (en milliers de tonnes)

Question 7 - Part a

Voir le tableau ci - dessus.