Question

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Explanation:

Step1: Determine the savings formula

Shawna starts with $200 and earns $120 per week. So the savings \( s \) after \( t \) weeks is \( s = 200 + 120t \).

Step2: Fill the table for part a

• For \( t = 0 \): \( s = 200 + 120(0) = 200 \)
• For \( t = 1 \): \( s = 200 + 120(1) = 320 \)
• For \( t = 2 \): \( s = 200 + 120(2) = 440 \)
• For \( t = 3 \): \( s = 200 + 120(3) = 560 \)
• For \( t = 4 \): \( s = 200 + 120(4) = 680 \)
• For \( t = 5 \): \( s = 200 + 120(5) = 800 \)
• For \( t = 6 \): \( s = 200 + 120(6) = 920 \)

So the table is:

Time in weeks	Savings
1	320
2	440
3	560
4	680
5	800
6	920

To graph, plot the points \((0, 200)\), \((1, 320)\), \((2, 440)\), \((3, 560)\), \((4, 680)\), \((5, 800)\), \((6, 920)\) and draw a line through them.

Step3: Solve part c

For week 1 and week 5:

• \((x_1, y_1)\): At \( t = 1 \), \( s = 320 \), so \((1, 320)\)
• \((x_2, y_2)\): At \( t = 5 \), \( s = 800 \), so \((5, 800)\)
• \( y_2 - y_1 = 800 - 320 = 480 \)
• \( x_2 - x_1 = 5 - 1 = 4 \)
• Slope \( = \frac{y_2 - y_1}{x_2 - x_1} = \frac{480}{4} = 120 \)

For week 3 and week 6:

• \((x_1, y_1)\): At \( t = 3 \), \( s = 560 \), so \((3, 560)\)
• \((x_2, y_2)\): At \( t = 6 \), \( s = 920 \), so \((6, 920)\)
• \( y_2 - y_1 = 920 - 560 = 360 \)
• \( x_2 - x_1 = 6 - 3 = 3 \)
• Slope \( = \frac{y_2 - y_1}{x_2 - x_1} = \frac{360}{3} = 120 \)

Filling the table:

	Using data for week 1 and week 5	Using data for week 3 and week 6
\((x_2, y_2)\)	\((5, 800)\)	\((6, 920)\)
\( y_2 - y_1 \)	480	360
\( x_2 - x_1 \)	4	3
Slope	120	120

Answer:

Part a Table:

Time in weeks	Savings
1	320
2	440
3	560
4	680
5	800
6	920

(Graph: Plot points \((0,200)\), \((1,320)\), \((2,440)\), \((3,560)\), \((4,680)\), \((5,800)\), \((6,920)\) and draw a line.)

Part c Table:

	Using data for week 1 and week 5	Using data for week 3 and week 6
\((x_2, y_2)\)	\((5, 800)\)	\((6, 920)\)
\( y_2 - y_1 \)	480	360
\( x_2 - x_1 \)	4	3
Slope	120	120