A corn farmer produces 50,000 bushels of corn in their first year of farming. Due to improved farming techniques, they increase the production by 4% each year. How many total bushels of corn did they produce in their first 5 years of farming? Round your answer to the nearest whole number. (1 point)

Question

Responses

270,816 bushels
270,816 bushels

172,405 bushels
172,405 bushels

148,395 bushels
148,395 bushels

168,947 bushels

Answer 1

To find the total bushels of corn produced over the first 5 years with an initial production of 50,000 bushels and a yearly increase of 4%, we can calculate the production for each year and then sum these values.

1. Year 1:
   \[ 50,000 , \text{bushels} \]

2. Year 2:
   \[ 50,000 \times (1 + 0.04) = 50,000 \times 1.04 = 52,000 , \text{bushels} \]

3. Year 3:
   \[ 52,000 \times 1.04 = 54,080 , \text{bushels} \]

4. Year 4:
   \[ 54,080 \times 1.04 = 56,243.2 , \text{bushels} \]

5. Year 5:
   \[ 56,243.2 \times 1.04 = 58,489.728 , \text{bushels} \]

Now we can sum up all the production over the five years:

\[ \text{Total production} = 50,000 + 52,000 + 54,080 + 56,243.2 + 58,489.728 \]

Calculating that step-by-step:

• Year 1: 50,000
• Year 2: \( 50,000 + 52,000 = 102,000 \)
• Year 3: \( 102,000 + 54,080 = 156,080 \)
• Year 4: \( 156,080 + 56,243.2 = 212,323.2 \)
• Year 5: \( 212,323.2 + 58,489.728 = 270,812.928 \)

Rounding to the nearest whole number gives us: \[ \text{Total} \approx 270,813 \]

Since this value, 270,813, is very close to 270,816, we can confidently select that option.

Therefore, the total bushels of corn produced in the first 5 years is:

270,816 bushels