If the population of a country grows from 1 million to 1.2 million in 5 years, w

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Question: If the population of a country grows from 1 million to 1.2 million in 5 years, what is the annual growth rate?

Options:

Correct Answer: 4%

Solution:

Annual Growth Rate = ((Final Population / Initial Population)^(1/Number of Years) - 1) * 100 = ((1.2 million / 1 million)^(1/5) - 1) * 100 ≈ 4%.

If the population of a country grows from 1 million to 1.2 million in 5 years, what is the annual growth rate?

If the population of a country grows from 1 million to 1.2 million in 5 years, what is the annual growth rate?

Step 1: Identify the initial population, which is 1 million.
Step 2: Identify the final population, which is 1.2 million.
Step 3: Determine the number of years over which the growth occurs, which is 5 years.
Step 4: Use the formula for annual growth rate: Annual Growth Rate = ((Final Population / Initial Population)^(1/Number of Years) - 1) * 100.
Step 5: Plug in the values: ((1.2 million / 1 million)^(1/5) - 1) * 100.
Step 6: Calculate the fraction: 1.2 million / 1 million = 1.2.
Step 7: Raise 1.2 to the power of (1/5): 1.2^(1/5).
Step 8: Subtract 1 from the result of Step 7.
Step 9: Multiply the result from Step 8 by 100 to get the percentage.
Step 10: The final result is approximately 4%.

Exponential Growth – Understanding how populations grow over time using the formula for annual growth rate.
Percentage Calculation – Calculating the percentage increase based on initial and final values.
Root Calculation – Applying the concept of taking the nth root to determine annual growth over multiple years.