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To solve this problem, we need to calculate the net percentage change in population over 4 years, given the successive changes of 20% increase, another 20% increase, 20% decrease, and then a final 20% decrease.

Let's denote the initial population as \( P \).

1. **First Year (20% Increase)**:
   \[
   P_1 = P \times 1.2 = 1.2P
   \]

2. **Second Year (20% Increase)**:
   \[
   P_2 = 1.2P \times 1.2 = 1.44P
   \]

3. **Third Year (20% Decrease)**:
   \[
   P_3 = 1.44P \times 0.8 = 1.152P
   \]

4. **Fourth Year (20% Decrease)**:
   \[
   P_4 = 1.152P \times 0.8 = 0.9216P
   \]

Now, we find the overall percentage change:
\[
\text{Percentage Change} = \left(\frac{P_4 - P}{P}\right) \times 100
\]
Substituting \( P_4 = 0.9216P \):
\[
\text{Percentage Change} = \left(\frac{0.9216P - P}{P}\right) \times 100 = (0.9216 - 1) \times 100 = -7.84\%
\]

So, the total change in population over the 4 years is a decrease of **7.84%**.

**Answer: Option (1) -7.84%**

Would you like a more detailed explanation or have any questions?

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### Additional Questions for Practice:

1. If there were a 10% increase each year instead of a 20% increase, what would the net change be?
2. What would be the total change if the sequence was 20% increase, 10% increase, 20% decrease, and 10% decrease?
3. How would the final percentage change differ if all changes were increases instead?
4. If only the last change was a decrease of 30% instead of 20%, what would the total change in percentage be?
5. What is the formula for calculating net changes in percentage for multiple successive percentage changes?

**Tip:** In successive percentage calculations, increasing and then decreasing by the same percentage does not bring you back to the original value due to compounding effects.

If there is 20% increase, then 20% increase, then 20% decrease and then 20% decrease in the population of a city in 4 successive years, then what will be the percentage of total change in population in 4 years?

Learn how to calculate the net percentage change in a city's population over 4 years with successive changes of 20% increase, 20% increase, 20% decrease, and 20% decrease. This problem explains key concepts in percentage change and compounding effects, suitable for students in Grades 10-12.

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