An apple farm installed a fish pond on its land to save money and increase potential revenue. Waste apples and...

Owning the Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

The dataset shows that integrating aquaculture with apple farming creates a beneficial feedback cycle. As fish production rises from \(0 \text{ to } 3500\) over five years, the cost of fertilizer per 10 kg of apples sold drops dramatically from \(\$0.05 \text{ to } \$0.005\). The average annual decrease in fertilizer cost is about \(\$0.01125 \text{ per year}\). The connection suggests fish waste effectively replaces externally purchased fertilizer. Fish production grows quickly in early years but the yearly increase slows after year 3 (from +1500/year to +500/year), indicating the system is maturing. Overall, the closed nutrient cycle increases profits by reducing outside costs and providing an additional product to sell.

Step-by-Step Solution

Question 1: Average Annual Decrease in Fertilizer Cost per 10 kg Apples

Complete Statement:

The average amount by which the cost of fertilizer per 10 kg of apples sold decreased from year 1 to year 5 is, to the nearest power of 10, nearest to _____ dollars per 10 kg apples per year.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: average amount by which the cost... decreased
  • Meaning: We are being asked to find the yearly average reduction in fertilizer cost over a period of time.
  • Relation to Chart: We need to use the fertilizer cost data given for the years 1 to 5.
  • Important Implications: This involves both subtracting and averaging over the time period.
• Statement Breakdown 2:
  • Key Phrase: from year 1 to year 5
  • Meaning: The calculation spans from the first to the fifth year.
  • Relation to Chart: We should read the cost values off the chart for year 1 and for year 5.
  • Important Implications: This is a time span of 4 years (\(5 - 1 = 4\)).

What is needed: The average yearly decrease in fertilizer cost per 10 kg apples, expressed as a single power of 10.

Solution:

• Condensed Solution Implementation:
  Subtract the fertilizer cost at year 5 from that at year 1 to find the total decrease, then divide by 4 to find the yearly average, and round to the nearest power of 10.
• Necessary Data points:
  Year 1 fertilizer cost: \(\$0.05\); Year 5 fertilizer cost: \(\$0.005\)
  • Calculations Estimations:
    Total decrease = \(\$0.05 - \$0.005 = \$0.045\); Years = 4; Average decrease = \(\$0.045 \div 4 = \$0.01125\)
  • Comparison to Answer Choices:
    \(\$0.01125\) is closest to 0.01 among the options provided.

FINAL ANSWER Blank 1: 0.01

Question 2: Rate of Growth in Fish Sold per Year after Year 3

Complete Statement:

After year 3, the rate of growth in the total number of fish sold per year was _____

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: After year 3
  • Meaning: We are concerned only with years 4 and 5, focusing on the trend following year 3.
  • Relation to Chart: Check the data points for fish sold in years 3, 4, and 5.
• Statement Breakdown 2:
  • Key Phrase: rate of growth in the total number of fish sold per year
  • Meaning: This is the yearly increase in number of fish sold.
  • Relation to Chart: Calculate the differences in fish sold between consecutive years after year 3.

What is needed: Whether the annual increases in the number of fish sold after year 3 are getting larger, smaller, or staying about the same.

Solution:

• Condensed Solution Implementation:
  Calculate and compare the increase from year 3 to 4, and from year 4 to 5.
• Necessary Data points:
  Year 3: 2000 fish; Year 4: 3000 fish; Year 5: 3500 fish
  • Calculations Estimations:
    Increase 3→4: \(3000 - 2000 = 1000\); Increase 4→5: \(3500 - 3000 = 500\); The increase is getting smaller.
  • Comparison to Answer Choices:
    Because the increase drops from 1000 to 500 fish, the rate of growth is decreasing.

FINAL ANSWER Blank 2: Decreasing

Summary

To solve these blanks, we looked at the trend data on the chart for both fertilizer cost and number of fish sold. For the first blank, we calculated the average annual decrease (\(\$0.01125\)) and rounded to the nearest power of 10, which is 0.01. For the second blank, we saw the annual increase in fish sold dropped from 1000 to 500 after year 3, so the answer is Decreasing. Both require extraction and comparison of values rather than complicated calculations.

Question Independence Analysis

Question 1 concerns the fertilizer cost trend while Question 2 concerns the trend in fish sales. Each is about a different quantity, requiring different information, so the blanks are independent and can be solved separately.