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A conservation program aims to increase the population of an endangered species

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Question: A conservation program aims to increase the population of an endangered species from 300 to 600 in 5 years. What is the required annual growth rate?

Options:

  1. 10%
  2. 15%
  3. 20%
  4. 25%

Correct Answer: 25%

Solution: 

To double the population in 5 years, the annual growth rate must be approximately 25%.

A conservation program aims to increase the population of an endangered species

Practice Questions

Q1
A conservation program aims to increase the population of an endangered species from 300 to 600 in 5 years. What is the required annual growth rate?
  1. 10%
  2. 15%
  3. 20%
  4. 25%

Questions & Step-by-Step Solutions

A conservation program aims to increase the population of an endangered species from 300 to 600 in 5 years. What is the required annual growth rate?
  • Step 1: Identify the current population of the species, which is 300.
  • Step 2: Identify the target population, which is 600.
  • Step 3: Calculate the total increase needed: 600 - 300 = 300.
  • Step 4: Determine the number of years for growth, which is 5 years.
  • Step 5: Use the formula for annual growth rate: (final population / initial population)^(1/number of years) - 1.
  • Step 6: Plug in the numbers: (600 / 300)^(1/5) - 1.
  • Step 7: Simplify the fraction: (2)^(1/5) - 1.
  • Step 8: Calculate (2)^(1/5), which is approximately 1.1487.
  • Step 9: Subtract 1 from 1.1487 to find the growth rate: 1.1487 - 1 = 0.1487.
  • Step 10: Convert 0.1487 to a percentage by multiplying by 100: 0.1487 * 100 = 14.87%.
  • Step 11: Round 14.87% to approximately 15% for easier understanding.
  • Exponential Growth – Understanding how populations grow over time and the formula for calculating growth rates.
  • Compound Interest Formula – Applying the formula for compound growth, which is relevant for calculating population increases.
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