Activity 5 - 1

1. Activity 5 - 1 Going Shopping

2. Objectives • Define growth factor • Determine growth factors from percent increases • Apply growth factors to problems involving percent increases • Define decay factor • Determine decay factors from percent decreases • Apply decay factors to problems involving percent decreases

3. Vocabulary • Growth Factor – a percentage increase in the original value of an item • Decay Factor – a percentage decrease in the original value of an item

4. Activity To earn revenue (income), many state and local governments require merchants to collect sales tax on the items they sell. In several localities, the sales tax is assessed at as much as 8% of the selling price and is passed on directly to the purchaser. Determine the total cost (including 8% sales tax) to the customer of the following items: a) Greeting card selling for $1.50 b) A DVD player selling for $300 1.50 + sales tax sales tax = 1.50  0.08 = 0.12 total = 1.50 + 0.12 = $1.62 300 + sales tax sales tax = 300  0.08 = 24 total = 300 + 24 = $324 • Many people correctly determine the total cost in two steps: • Compute the sales tax of the item • Add the sales tax to the selling price to obtain the total cost

5. Growth Factors • Growth factor problems are when the ratio of the new value to the original value is always the same and the values are increasing. This ratio is the growth factor. • Growth factor = 1 + percentage growth Original value × growth factor = new value

6. Growth Factor Example 1 Determine the growth factor represented by the following percent increases • 30% • 75% • 15% • 5.5% Growth factor = 1 + 0.3 = 1.30 Growth factor = 1 + 0.75 = 1.75 Growth factor = 1 + 0.15 = 1.15 Growth factor = 1 + 0.055 = 1.055

7. Growth Factor Example 2 Determine the new values given the growth factor • $400 and 50% increase • 120,000 people and a 30% increase Growth factor = 1 + 0.5 = 1.5 400 × 1.5 = 600 Growth factor = 1 + 0.3 = 1.3 120,000 × 1.3 = 156,000

8. Growth Factor Example 3 Determine the growth factor for any quantity that increases 20%. Use the growth factor to determine this year’s budget if last year’s was $75,000 Growth factor = 1 + 0.2 = 1.2 Growth factor = 1 + 0.2 = 1.2 75,000 × 1.2 = 90,000

9. Decay Factors • Decay factor problems are when the ratio of the new value to the original value is always the same, but the values are decreasing. This ratio is the decay factor. • Decay factor = 1 - percentage decay Original value × decay factor = new value

10. Decay Factor Example 1 Determine the decay factor represented by the following percent decreases • 30% • 75% • 15% • 5.5% Decay factor = 1 – 0.3 = 0.7 Decay factor = 1 – 0.75 = 0.25 Decay factor = 1 – 0. 15 = 0.85 Decay factor = 1 – 0.055 = 0.945

11. Decay Factor Example 2 Determine the new values given the decay factor • $400 and 20% decrease • 120,000 people and a 12% decrease Decay factor = 1 – 0.2 = 0.8 400 × 0.8 = 320 Decay factor = 1 – 0.12 = 0.88 120,000 × 0.88 = 105,600

12. Decay Factor Example 3 Determine the original price of an answering machine if you got a 40% discount and paid $150. Determine the original price of a Nordic Track if you got a 25% discount and paid $1140. Decay factor = 1 – 0.4 = 0.6 original × 0.6 = 150 Original = (150/0.6) = 250 Decay factor = 1 – 0.25 = 0.75 original × 0.75 = 1140 Original = (1140/0.75) = 1520

13. Summary and Homework • Summary • The growth factor is when things increase: • is the ratio new / original value • formed by adding specified percent increase to 100% and then changing to decimal form • original value  growth factor = new value • new value  growth factor = original value • The decay factor is when things decrease: • is the ratio new / original value • formed by subtracting specified percent decrease from 100% and then changing to decimal form • original value  decay factor = new value • new value  decay factor = original value • Homework • pg 533 – 37; problems 1 – 3, 5, 10 – 12, 15