5-Minute Check on Activity 5-1

1. 5-Minute Check on Activity 5-1 Determine the growth factor for a 30% increase Determine the growth rate for 1.53 Determine the decay factor for a 16% decrease Determine the decay rate for 0.81 What is the growth factor if gas goes from 3.25 / gal to 4.25 / gal? What is the decay factor if gas goes from 4.75 / gal to 4.00 / gal? G-factor = 1 + 0.3 = 1.30 G-rate = 1 – 1.53 = 0.53 or 53% D-factor = 1 – 0.16 = 0.84 D-rate = 1 – 0.81 = 0.19 or 19% G-factor = 4.25/3.25 ≈ 1.31 D-factor = 4.00/4.75 ≈ 0.84 Click the mouse button or press the Space Bar to display the answers.

2. Activity 5 - 2 Take an Additional 20% Off

3. Objectives • Define consecutive growth and decay factors • Determine a consecutive growth or decay factor from two or more consecutive percent change • Apply consecutive growth or decay factors from to solve problems involving percent changes

4. Vocabulary • Cumulative Factors – the consecutive growth or decay factors from two or more consecutive percent changes

5. Activity Your friend arrives at you house. Today’s newspaper contains a 20% off coupon at Old Navy. The $100 jacket she had been eyeing all season was already reduced by 40%. She clipped the coupon, drove to the store, selected her jacket and walked up to the register. The cashier brought up a price of $48; your friend insisted that the price should have been only $40. The store manager arrived and re-entered the transaction, and again the registered displayed $48. Your friend left without purchasing the jacket and drove straight to your house to tell you her story. How do you think your friend calculated a price of $40? 20 + 40 = 60% off 100 × (1 – 0.6) = 40

6. Activity cont You grab a pencil and start your own calculation. First you determine the ticketed price that reflects the 40% reduction. At what price is Old Navy selling the jacket? Explain how you calculated this price. To what price does the 20%-off coupon apply? Apply the 20% discount to determine the final price of the jacket. If you applied the discounts in reverse order, that is, applying the 20% coupon, followed by a 40% reduction, would the final sales price change? 100 × (1 – 0.4) = 60 60 dollars 60 × (1 – 0.2) = 48 No

7. Cumulative Factors You can form a single decay (or growth) factor that represents the cumulative effect of applying the consecutive factors; the single decay factor is the product of the three decay factors. For example: a 10% off coupon on top of 25% off all Holiday items yields (1 – 0.10)(1 – 0.25) = (0.9)(0.75) = (0.675)

8. Cumulative Factors Example 1 A stunning $2000 gold and diamond necklace you saw was far too expensive to even consider. However, over several weeks you tracked the following successive discounts: 20% off list; 30% off marked price; and an additional 40% off every item. Determine the selling price after each of the discounts is taken. 2000 × (1 – 0.2) = 1600 1600 × (1 – 0.3) = 1120 1120 × (1 – 0.4) = 672

9. Cumulative Factors Example 2 You spent $657 on a HD TV that was on sale for 30% off and you had a rewards bonus of an additional 10% off. How much did the HDTV cost originally? 657 × (1+ 0.3) = 854.10 845.10 × (1 + 0.1) = 939.51

10. Cumulative Factors Example 3 You purchased $1000 of a recommended stock last year and watched gleefully as it rose quickly by 30%. Unfortunately, the economy turned downward, and your stock recently fell 30% from last year’s high. Have you made or lost money on your investment? 1000 × (1+ 0.3) = 1300 1300 × (1 – 0.3) = 910 1000 – 910 = 90 dollar loss

11. Summary and Homework • Summary • Cumulative effect of a sequence of percent changes is the product of the associated growth or decay factors • Cumulative effect of a sequence of percent changes is the same regardless of the order the changes are applied • Homework • pg 542; problems 1 – 6