Multiple choice

A population grows at the rate of $5 \%$ per year. Then the population will be doubled at

  1. $10\log 2\,years$
  2. $20\log 2\,years$
  3. $30\log 2\,years$
  4. $40\log 2\,years$
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B Correct answer
AI explanation

Using the compound interest formula for population growth, the population after t years is P multiplied by (1 + r) to the power of t. Setting the final population as 2P, r as 0.05, and taking the natural logarithm of both sides yields t multiplied by ln(1.05) equals ln(2). Solving for t gives a doubling time of approximately 13.86 years, which is 20 multiplied by log(2). The result is 20 log 2 years.

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