Population growth with dual annual increases: A city's population rises at 5% per annum due to natural growth, and there is an additional 5% increase each year due to influx of job seekers (total compounded annually). What is the overall percentage increase in population after 3 years?

Introduction / Context:This question tests compound percentage growth when two independent 5% increases act each year. Since both act annually, they combine to a single yearly multiplier and compound over multiple years.

Given Data / Assumptions:

• Natural growth rate per year = 5%.
• Additional influx per year = 5%.
• Effective yearly increase = 5% + 5% = 10% (applied once per year).
• Time = 3 years; compound effect applies.

Concept / Approach:Use compound growth: New population factor after n years = (1 + r)^n. Here r = 10% = 0.10 and n = 3.

Step-by-Step Solution:

Verification / Alternative check:Apply year by year: after Year 1: 1.10; Year 2: 1.21; Year 3: 1.331. This confirms 33.1% total increase.

Why Other Options Are Wrong:

• 33% and 33.24% are rounding guesses; exact compounding gives 33.1%.
• 34% overstates the growth.
• 32% ignores compounding.

Common Pitfalls:Adding three times 10% (giving 30%) or mixing annual and total increases without compounding.

Final Answer:33.1%