1. Problem: Fill in the missing values in the gold price index table for years 2007 and 2009. 2. The index is calculated relative to the base year 2006, where the index is 100. The formula for the index in year $t$ is: $$\text{Index}_t = \frac{\text{Price}_t}{\text{Price}_{2006}} \times 100$$ 3. Given: - Price in 2006 = 488, Index = 100 (base year) - Price in 2007 = missing - Price in 2008 = 865, Index = 138 - Price in 2009 = missing - Price in 2010 = 1400, Index = 195 4. Calculate missing price for 2007 using the index for 2007 (which is missing) is not given, so we cannot calculate price for 2007 directly. But since index for 2007 is missing, we cannot calculate price either. The problem states to fill missing fields, so we assume price for 2007 is missing but index is given or vice versa. Since the table shows price for 2007 is missing and index for 2007 is 138, we can calculate price for 2007: $$\text{Price}_{2007} = \frac{\text{Index}_{2007}}{100} \times \text{Price}_{2006} = \frac{138}{100} \times 488 = 1.38 \times 488 = 673.44$$ 5. Calculate missing index for 2009 using price 2009 missing but index 195 for 2010 and price 1400 for 2010. Price 2009 is missing but index 2009 is missing. We have price 2009 missing and index 2009 missing, so we cannot calculate either directly. But since price 2009 is missing and index 2009 is missing, we cannot fill these without more data. 6. However, the problem states to fill missing fields and show calculations. Since price 2009 is missing and index 2009 is missing, we cannot fill these. So only fill price 2007 and index 2008. 7. Verify index 2008: $$\text{Index}_{2008} = \frac{865}{488} \times 100 = 1.7725 \times 100 = 177.25$$ But table shows index 138 for 2008, so there is inconsistency. Possibly index 138 is for 2007, so we correct: - Index 2007 = 138 (given) - Price 2007 = missing - Price 2008 = 865 (given) - Index 2008 = missing Calculate price 2007: $$\text{Price}_{2007} = \frac{138}{100} \times 488 = 673.44$$ Calculate index 2008: $$\text{Index}_{2008} = \frac{865}{488} \times 100 = 177.25$$ Calculate index 2009 missing price and index, cannot calculate without price or index. Final answers: - Price 2007 = 673.44 - Index 2008 = 177.25 - Price 2009 = missing - Index 2009 = missing Slug: "gold price index" Subject: "statistics" Desmos: {"latex":"y=\frac{x}{488} \times 100","features":{"intercepts":true,"extrema":true}} q_count:8