`{:("Month","Number of Peppers"),("June","2,200"),("July","2,640"):}`
A farmer counted the number of peppers produced by a certain field in June and July. The number counted for each month was recorded in the table above. The farmer estimates the percent increase from June and July would be half the the percent increase From July to August. How many peppers does the farmer expect the field to produce in August?

Options

A. 2860
B. 2904
C. 3520
D. 3696

Answer

To solve the problem step by step, we will calculate the percentage increase from June to July and then use that information to find the expected number of peppers in August.

### Step 1: Calculate the percentage increase from June to July
We have the following data:
- Number of peppers in June = 2,200
- Number of peppers in July = 2,640

The formula for percentage increase is:
\[ \text{Percentage Increase} = \frac{\text{Final Amount} - \text{Initial Amount}}{\text{Initial Amount}} \times 100 \]

Substituting the values:
\[ \text{Percentage Increase} = \frac{2640 - 2200}{2200} \times 100 \]

Calculating the difference:
\[ 2640 - 2200 = 440 \]

Now substituting back into the formula:
\[ \text{Percentage Increase} = \frac{440}{2200} \times 100 \]

Calculating:
\[ \frac{440}{2200} = 0.2 \quad \text{(which is 20% when multiplied by 100)} \]

So, the percentage increase from June to July is **20%**.

### Step 2: Determine the percentage increase from July to August
According to the problem, the farmer estimates that the percentage increase from June to July (20%) is half of the percentage increase from July to August. Therefore, the percentage increase from July to August will be:
\[ \text{Percentage Increase from July to August} = 2 \times 20\% = 40\% \]

### Step 3: Calculate the expected number of peppers in August
Now, we need to find out how many peppers the farmer expects to produce in August using the percentage increase of 40%.

Using the initial amount for July (2,640), we calculate the increase:
\[ \text{Increase} = \text{Initial Amount} \times \frac{\text{Percentage Increase}}{100} \]
Substituting the values:
\[ \text{Increase} = 2640 \times \frac{40}{100} = 2640 \times 0.4 = 1056 \]

### Step 4: Calculate the expected number of peppers in August
Now, we add the increase to the initial amount for July:
\[ \text{Expected Amount in August} = \text{Initial Amount in July} + \text{Increase} \]
Substituting the values:
\[ \text{Expected Amount in August} = 2640 + 1056 = 3696 \]

Thus, the farmer expects the field to produce **3,696 peppers** in August.

### Final Answer:
The expected number of peppers in August is **3,696**.

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