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The annual production of honey in 2017 was 50 kg, and in 2022 it was 150 kg. It's annual
honey production increases by the same amount every year. By which formula can it be calculated
annual honey production where t is the number of years after 2017? One of the answers in the picture is correct. Resolve this using clear step by step instructions and pretend I am a ten year old

To solve this problem, we'll determine the correct formula for calculating the annual honey production \( m(t) \) where \( t \) is the number of years after 2017.

### Step-by-Step Explanation:

1. **Understand the problem**: 
   - In 2017 (when \( t = 0 \)), the honey production was 50 kg.
   - In 2022 (when \( t = 5 \)), the honey production was 150 kg.
   - We know that the production increases by the same amount every year.

2. **Find the increase per year**:
   - The total increase in honey production from 2017 to 2022 is \( 150 \, \text{kg} - 50 \, \text{kg} = 100 \, \text{kg} \).
   - This increase happened over 5 years (from 2017 to 2022), so the increase per year is:
     \[
     \frac{100 \, \text{kg}}{5 \, \text{years}} = 20 \, \text{kg/year}
     \]

3. **Write the formula**:
   - The honey production increases by 20 kg every year. So if we start with 50 kg in 2017 and increase by 20 kg each year, the formula for honey production \( m(t) \) after \( t \) years is:
     \[
     m(t) = 20t + 50
     \]

4. **Match with the options**:
   - We check the options given:
     - **A**: \( m(t) = 3t + 50 \) 
     - **B**: \( m(t) = 3t + 150 \)
     - **C**: \( m(t) = 20t + 50 \)
     - **D**: \( m(t) = 20t + 150 \)
   - The correct formula we derived is \( m(t) = 20t + 50 \).

### **Conclusion**:
The correct answer is **C**.

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Would you like more details or have any questions? Here are five related questions to explore further:

1. How would the formula change if the honey production started at 100 kg in 2017?
2. What would be the honey production in 2025 using the correct formula?
3. How does a linear equation like this one differ from a quadratic equation?
4. Can you explain how the rate of increase per year affects the overall formula?
5. If the increase per year was 30 kg instead of 20 kg, what would the new formula be?

**Tip**: When trying to write a formula for something that changes consistently over time, think about the starting point (initial value) and how much it changes each time period (the rate of change).

Learn how to calculate annual honey production increase over time starting from 2017 with a clear step-by-step solution. Understand the formula for annual honey production based on given initial and final production values. Suitable for students in Grades 5-7.

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