4.7.1: Preparation 4.7

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(1) Kim is trying to do a better job of managing her money. A book on personal finance recommends that she track how much she spends on different items. Kim knows she spends a lot on “nonessentials” such as buying a cup of coffee or buying small items from street vendors. She finds it hard to track these purchases so she decides to set aside a certain amount of money in cash that she will use for these purchases. Every Sunday, she records how much she has left. She keeps a record for 10 weeks. Her data are approximately linear so she made the following graph in which she extends the model past 10 weeks.

Line graph showing the non-essential expenses.

Y-axis represents the amount left to spend in dollars, ranging from 0 to 600.
X-axis represents the number of weeks, ranging from 0 to 25.

0 = 500
5 = in between 300 and 400
10 = in between 200 and 300
15 = in between 100 and 200
20 = 0

(a) Complete the table below by matching the following mathematical terms to the appropriate contextual meaning and estimating the values from the graph.

Slope
Vertical intercept
Horizontal intercept

Contextual Meaning	Mathematical Term	Value (including units)
Amount Kim sets aside for non-essential items
Time it takes Kim to spend the entire amount
Amount Kim spends per week

(b) Write an equation for the model. Let A = amount left to spend ($), and w = the number of weeks.

(2) In many computer applications such as spreadsheets, a power is indicated by a caret symbol (^). For example, 3⁴ would be written as 3^4. As a part of her budget management, Kim has put money into an Individual Retirement Account. She creates a spreadsheet to estimate her earnings over time.
She enters the formula: $= 1500*\left( 1 + \dfrac{0.06}{4}\right)\wedge(4 * A2)$, where A2 = the time in years.

(a) How much did Kim invest?

(b) What annual rate of interest does she expect to earn over time? Write your answer as a percentage.

(i) Annual

(ii) Quarterly

(iii) Monthly

(iv) Daily

After Preparation 4.7 (survey)

You should be able to do the following things for the next collaboration. Rate how confident you are on a scale of 1–5 (1 = not confident and 5 = very confident).

Before beginning Collaboration 4.7, you should understand the concepts and demonstrate the skills listed below.

Skill or Concept: I can …	Rating from 1 to 5
create and use linear equations, including understanding of vertical and horizontal intercepts and slope in the context of a problem.
create and use exponential equations, including understanding of vertical intercept and percentage change in the context of an interest-bearing account.

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