Economists study the way society uses its resources. One important resource studied is agriculture. The recent increase in demand for organic produce has created some interesting economic scenarios for both farmers and consumers. Click the article to learn key facts about the economics of organic produce and answer a few questions.

Question

Which is a reason that organic farming is more expensive than conventional farming?

How many years must a farm be run organically before its produce can be labeled as “organic”?

What is a benefit of crop rotation?

Next time you are at the grocery store, take a minute to compare prices in the produce section. You will probably see that organic produce costs significantly more than produce that is conventionally grown. Let’s explore why organic produce comes with a higher price tag.

The primary reason for the higher price of organic produce is simple: it costs more to grow organic fruits and vegetables. Perhaps you are thinking, “Wait a minute! How can it cost more to grow food without chemical pesticides and fertilizers? Wouldn’t the organic farmer actually save money?” Let’s dig deeper to get a better understanding of the costs associated with organic farming.

First, farms must be certified organic through the National Organic Program before they can sell their produce as organic. The certification process is complex, requiring three years of inspections and organic practices before the certification is granted. This transition costs farmers a lot of money as their organic crops result in less produce, but they cannot yet sell their produce as organic. Without organic certification, farmers in transition cannot reap the benefits of higher prices for organic goods. The result is a loss of revenue. Organic certification is also expensive. In addition to an initial fee, there are annual recurring certification costs. Some farmers have reported an annual cost of $150 per acre.

Several other factors also increase the cost of organic farming. Organic seeds, for example, may produce lower yields or be more vulnerable to pests and disease than crops grown from genetically modified seeds. Organic farmers may compensate by hiring more workers to remove pests and weeds by hand. Organic farmers also use crop rotation. Crop rotation is a practice that involves the raising of different crops on the same land in succession. The purpose of this practice is to build healthy soil so that it is ready later to grow more profitable crops, like tomatoes or strawberries.

So how much would it cost to operate an organic farm? Table 1 shows a sample cost of producing second-year strawberries on a one-acre organic farm. Operating costs include fertilization, irrigation, hand weeding, and harvesting operations such as the cooling of harvested products. Cash overhead refers to business expenses not related to what the business sells. This includes office expenses and sanitation fees. Table 2 shows the cost of the activities mentioned over a seven-month period.

Cost Source Cost in U.S. Dollars
Operating Costs/Acre $27,576
Cash Overhead $4,873
TOTAL CASH COSTS/ACRE $32,449
Table 1. Costs per Acre to Produce Second Year Strawberries

Cost Source Cost Per Month in U.S. Dollars
March April May June July August September
Operation
Fertilize (Drip) 91 88 88 88 88 88 88
Irrigate: production season (Drip) 58 81 81 81 81 81 81
Weed hand 121 121 121 121 121 121 121
Harvest fresh 1,308 2,082 2,082 3,118 3,118 2,296 1,142
Cooling fresh 125 250 250 375 375 250 125
Cash Overhead
Office expenses 63 63 63 63 63 63 63
Sanitation fee 17 17 17 17 17 17 17
Table 2. Costs of Some Farming Activities over a Seven-Month Period
Organic farming is costly. Certifications, lower yields, higher costs, and fewer subsidies—these are all factors that help explain why organic produce often costs more than produce that is conventionally grown. Despite the costs, the demand for organic produce is increasing because people are becoming more aware of the benefits of eating organic food.

So, the next time you see organic produce being sold for twice the price of its conventional equivalent, you will have a better understanding of what you are paying for.

Answer 1

Here are the answers to your questions based on the article:

1. Which is a reason that organic farming is more expensive than conventional farming?

   • One reason organic farming is more expensive is that the certification process requires three years of inspections and organic practices before a farm can sell produce as organic, during which time farmers may incur losses due to lower yields.

2. How many years must a farm be run organically before its produce can be labeled as “organic”?

   • A farm must be run organically for three years before its produce can be labeled as “organic.”

3. What is a benefit of crop rotation?

   • A benefit of crop rotation is that it helps build healthy soil, preparing it for growing more profitable crops in the future, such as tomatoes or strawberries.

Answer 2

Which is a reason that organic farming is more expensive than conventional farming?

✔ Organic farmers must pay for a costly certification process.

How many years must a farm be run organically before its produce can be labeled as “organic”?

✔ 3

What is a benefit of crop rotation?

✔ Rotating crops can help build healthy soil.

Use the information in the article and associated document about organic strawberry farming to answer the questions about sales appropriation.

The document is located at this article.

Use the data table towards the end of the article to answer the questions.

The total operating cost to run the organic strawberry farm varies directly with its number of acres. What is the constant of variation in this scenario?

If the total operating cost for a 20-acre organic strawberry farm is $551,520, how many acres are on a farm with a total operating cost of $441,216?

acres

the article we used

Answer 3

To determine the constant of variation and answer the related questions, we can refer to the costs provided in the article for organic strawberry farming.

1. What is the constant of variation in this scenario?

From Table 1, it shows that the operating cost per acre is $27,576.

To find the constant of variation (k), we can represent the total operating cost (C) in relation to the number of acres (A): \( C = k \times A \)

We already know that \( k = 27,576 \).

2. If the total operating cost for a 20-acre organic strawberry farm is $551,520, how many acres are on a farm with a total operating cost of $441,216?

First, let's verify the operating cost for the 20-acre farm: \[ C = k \times A \] \[ C = 27,576 \times 20 = 551,520 \] This confirms that the calculation is correct.

Now, to find out how many acres correspond to a total cost of $441,216, we can set up the following equation: \[ 441,216 = 27,576 \times A \] To solve for A: \[ A = \frac{441,216}{27,576} \] \[ A = 16 \]

So, the answers are:

1. The constant of variation is $27,576.
2. A farm with a total operating cost of $441,216 has 16 acres.

Answer 4

There are so many little things that go into organic farming and each of them adds additional costs.

Some of these additional costs are listed in the article located here.

Use the data table at the end of the document to answer the questions.

Which cost category in the table shows an example of direct variation?

The total cost for office expenses to run the organic strawberry farm varies directly with the number of months it is used. Which equation represents this scenario?

What would be the total cost for office expenses for 24 months?

Answer 5

To address your questions, let's analyze the information based on the context provided:

1. Which cost category in the table shows an example of direct variation?

The office expenses category shows an example of direct variation with respect to the number of months. As office expenses are fixed costs that are incurred monthly, they vary directly with time (the number of months).

2. Which equation represents this scenario?

Looking at the data provided, the monthly office expenses are $63. The total cost (C) for office expenses based on the number of months (M) can be expressed with the equation: \[ C = 63 \times M \]

3. What would be the total cost for office expenses for 24 months?

To calculate the total cost for office expenses for 24 months, we can substitute \( M = 24 \) into the equation: \[ C = 63 \times 24 \] Calculating the total: \[ C = 1,512 \]

Final Answers:

1. Cost category that shows direct variation: Office expenses.
2. Equation representing the scenario: \( C = 63 \times M \).
3. Total cost for office expenses for 24 months: $1,512.

Answer 6

for the Which cost category in the table shows an example of direct variation? options are weed-hand and Fertilize:(drip)

Answer 7

Given the options provided—weed-hand and Fertilize (drip)—we can determine which of these cost categories shows direct variation with respect to the number of months or the amount of product used.

Analyzing the Options:

1. Weed-hand:

   • The cost for hand weeding is given as a fixed amount per month, specifically $121 each month across the months listed (from March to September). Thus, this cost varies directly with the number of months, making it a candidate for direct variation.

2. Fertilize (drip):

   • The cost for fertilization (drip) is also given as a fixed monthly amount of $88 each month, making it another candidate for direct variation.

Conclusion:

Both weed-hand and Fertilize (drip) show examples of direct variation with the number of months. However, if you must choose one, either can be correct as they both present fixed costs that vary directly with time.

If you are required to select only one based on context or any specific conditions provided, weed-hand is commonly associated with direct labor, which can make it a more prominent example of direct variation due to its relation to the actual work done each month. Thus, you may consider choosing:

Weed-hand as the cost category that shows an example of direct variation, given the context of labor variances in organic farming practices.

Answer 8

Which cost category in the table shows an example of direct variation?

✔ Weed-hand

The total cost for office expenses to run the organic strawberry farm varies directly with the number of months it is used. Which equation represents this scenario?

✔ y = 63x

What would be the total cost for office expenses for 24 months?

✔ $1,512.00

Organic foods in local stores are typically more expensive than conventional foods.The table below compares recent organic and conventional prices per pound for carrots and apples. Use the table to answer the questions.A table showing the first column, Organic Price and the second column, Conventional Price. The first row is Carrots with the entries, $1.51 per pound and $0.77 per pound. The second row is Apples with the entries $2.34 per pound and $1.57 per pound. The third row is Onions with the entries $1.57 per pound and $0.93 per pound.Do the organic prices vary directly with the conventional prices? If so, identify k.Does the total cost of organic apples vary directly with the number of pounds of organic apples purchased? If so, identify k.

Answer 9

To determine whether the organic prices vary directly with the conventional prices, and whether the total cost of organic apples varies directly with the number of pounds purchased, let's analyze the data provided in the table:

Price Comparison Table:

• Carrots:

  • Organic Price: $1.51 per pound
  • Conventional Price: $0.77 per pound

• Apples:

  • Organic Price: $2.34 per pound
  • Conventional Price: $1.57 per pound

• Onions:

  • Organic Price: $1.57 per pound
  • Conventional Price: $0.93 per pound

Part 1: Do the organic prices vary directly with the conventional prices?

To check for direct variation, we can find the ratio of organic price to conventional price for each type of produce (let's denote organic price as \( O \) and conventional price as \( C \)):

1. Carrots: \[ k = \frac{O}{C} = \frac{1.51}{0.77} \approx 1.96 \]

2. Apples: \[ k = \frac{O}{C} = \frac{2.34}{1.57} \approx 1.49 \]

3. Onions: \[ k = \frac{O}{C} = \frac{1.57}{0.93} \approx 1.69 \]

Conclusion for Part 1:

• Since the ratio \( k \) is not constant across all three products, the organic prices do not vary directly with the conventional prices.

Part 2: Does the total cost of organic apples vary directly with the number of pounds of organic apples purchased?

Yes, the total cost of organic apples does vary directly with the number of pounds purchased. The equation for direct variation is given by: \[ y = kx \] Where \( y \) is the total cost, \( k \) is the price per pound, and \( x \) is the number of pounds.

For organic apples:

• Price per pound \( k = 2.34 \)

Thus, the equation representing this scenario is: \[ y = 2.34x \] Where:

• \( y \) is the total cost of organic apples.
• \( x \) is the number of pounds purchased.

Final Answers:

1. Do the organic prices vary directly with the conventional prices?

   • No, they do not vary directly since \( k \) is not constant across the products.

2. Does the total cost of organic apples vary directly with the number of pounds purchased?

   • Yes, it does.
   • The equation is: \( y = 2.34x \).

Answer 10

Do the organic prices vary directly with the conventional prices? If so, identify k.

✔ No, this is not direct variation.

Does the total cost of organic apples vary directly with the number of pounds of organic apples purchased? If so, identify k.

✔ Yes, this is direct variation with k = 2.34.

Which graphs show functions with direct variation? Select three options.A coordinate plane showing Parking Garage Rates with Time in hours on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2.4) and (5, 4).A coordinate plane showing Cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5).A coordinate plane showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).

2. Which sequence is generated by the function f(n + 1) = f(n) – 2 for f(1) = 10?

–10, –12, –14, –16, –18, ...
–2, 8, 18, 28, 38, ...
8, 18, 28, 38, 48, ...
10, 8, 6, 4, 2, ...

3. The points (3, 24) and (7, 56) represent points of a function where y, the number of photographs, varies directly with x, the number of pages in an album. Which statement describes another point on the graph of this function?

A 50-page photo album holds 400 photographs.
An 80-page photo album holds 560 photographs.
A 100-page photo album holds 8,000 photographs.
A 900-page photo album holds 8,400 photographs.

4. Which graph represents a function with direct variation?A coordinate plane with a U shaped line graphed with the minimum at (0, 0).A coordinate plane with a V shaped line graphed with the minimum at (0, 0).A coordinate plane with a line passing through (negative 4, 2), (0, 0) and (4, negative 2).A coordinate plane with a line passing through (negative 2, negative 3), (0, 1) and (1, 3).

5. The graph represents the direct variation function between earnings in dollars and hours worked. A coordinate plane showing Store Clerk Pay, Hours Worked on the x-axis and Total Earnings in dollars on the y-axis. A line starting at (0, 0) and passing through (4, 30), (8, 60) and (12, 90)Which equation can be used to describe the direct variation function between E, the total earnings in dollars, and h, the number of hours worked?E = 1.5hE = 7.5hE = 13hE = 15h

6. A catering company uses different functions to estimate the itemized costs for a party. The table below represents the included tip for wait staff as a function of the number of guests served.A table showing Catering Cost for Wait Staff Gratuity with two columns and 6 rows. The first column has, Number of Guests, and has the entries, 10, 20, 30, 40, 50. The second column, Wait Staff Tip, has the entries, $18, $36, $54, $72, $90.If the tip varies directly with the number of guests, which equation represents the relationship between the tip, t, and the number of guests, g?t = 1.8gt = t equals StartFraction g Over 18 EndFraction.g = 1.8tg = g equals StartFraction t Over 18 EndFraction.

7. A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function?
y=-4/3x
y=-3/4x
y=3/4x
y=4/3x

8. The table represents a bicycle rental cost in dollars as a function of time in hours.A table showing Bicycle Rental with 2 columns and 6 rows. The first column, Time in hours, has the entries, 0, 2, 4, 6, 8. The second column, cost in dollars, has the entries, 0, 10, 20, 30, 40.Which explains whether or not the function represents a direct variation?This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.This function represents a direct variation because it has a positive, constant rate of change of $10 per hour.This function does not represent a direct variation because it does not represent the cost for 1 hour.This function does not represent a direct variation because the function rule for the cost is to add $10, not multiply by a constant.

9. A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?
y=x/14
y=x/7
y=7x
y=14x

10. The sequence below represents Marisa’s fine at the library for each day that she has an overdue book:

$0.50, $0.65, $0.80, $0.95, $1.10, ...

Which equation represents Marisa’s library fine as a function of a book that is n days overdue?

f(n) = 0.15n
f(n) = 0.50n
f(n) = 0.15n + 0.35
f(n) = 0.50n + 0.15

Answer 11

Here are the answers to your questions based on the provided scenarios and information:

1. Which graphs show functions with direct variation? Select three options.

Based on the descriptions, functions with direct variation are linear functions that pass through the origin (0,0) and have a constant rate of change.

• Parking Garage Rates: This is direct variation since it shows a linear relationship starting from (0,0).
• Cost of Cinnamons: This shows a direct variation as it likely starts from (0,0) based on price per ounce.
• Breakfast Cost: This likely shows direct variation if it's a linear relationship. Depending on context, we might assume it's direct since many meals would cost more.

More certainty on the options might be needed for the last one. If the fourth option with "Ferry Ride Cost" passes through the origin, it will also be valid.

2. Which sequence is generated by the function \( f(n + 1) = f(n) - 2 \) for \( f(1) = 10 \)?

For \( f(1) = 10 \):

• \( f(2) = f(1) - 2 = 10 - 2 = 8 \)
• \( f(3) = f(2) - 2 = 8 - 2 = 6 \)
• \( f(4) = f(3) - 2 = 6 - 2 = 4 \)
• \( f(5) = f(4) - 2 = 4 - 2 = 2 \)

Thus, the sequence is:

• 10, 8, 6, 4, 2, ...

3. The points (3, 24) and (7, 56) represent points of a function where \( y \), the number of photographs, varies directly with \( x \), the number of pages in an album. Which statement describes another point on the graph of this function?

To find the constant rate of variation:

• From \( (3, 24) \): \( k = \frac{24}{3} = 8 \)
• From \( (7, 56) \): \( k = \frac{56}{7} = 8 \)

So the relationship \( y = 8x \).

Checking the options:

• A 50-page album: \( y = 8(50) = 400 \) photographs.
• An 80-page album: \( y = 8(80) = 640 \) photographs.
• A 100-page album: \( y = 8(100) = 800 \) photographs.
• A 900-page album: \( y = 8(900) = 7200 \) photographs.

Thus, the correct option is:

• A 50-page photo album holds 400 photographs.

4. Which graph represents a function with direct variation?

To show direct variation, a graph must linearly pass through the origin.

• The graph with a line passing through (0, 0) is the only valid representation of direct variation in the options.

5. The graph represents the direct variation function between earnings in dollars and hours worked. Which equation can be used to describe this function?

From the context:

• At \( (4, 30) \), the rate is \( \frac{30}{4} = 7.5 \)
• At \( (8, 60) \), the rate is also consistent \( 60/8 = 7.5 \)
• Thus, the equation is \( E = 7.5h \).

6. If the tip varies directly with the number of guests, which equation represents the relationship between the tip, \( t \), and the number of guests, \( g \)?

Check the unit rate using given data:

• From the table: $18 for 10 guests → $1.8 per guest.
• The equation is:
  • \( t = 1.8g \).

7. A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function?

To find \( k \):

• \( k = \frac{y}{x} \)
• Using (12, 9): \[ k = \frac{9}{12} = \frac{3}{4} \]

Thus, the equation representing the function is:

• \( y = \frac{3}{4}x \).

8. The table represents bicycle rental cost as a function of time in hours. Which explains whether or not this function represents direct variation?

Check points:

• \( (0, 0) \) shows passing through the origin and the cost increases consistently by $10, so:
• This function represents a direct variation because it passes through the origin and has a constant rate of change of $10 per hour.

9. A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?

Using the same method:

• \( k = \frac{14}{2} = 7 \)
• Thus, the equation is:
• \( y = 7x \).

10. Which equation represents Marisa’s library fine as a function of days overdue?

Looking at the sequence:

• The difference between fines is $0.15 each day.
• Starting at $0.50 for the first day, so,
• \( f(n) = 0.15n + 0.35 \) represents the fine for \( n \) days overdue.

Feel free to let me know if you need further clarification on any of the options!