Question:medium

It took 168 years for a population to increase from 0.4 million to 3.2 million. If we assume exponential growth at a constant rate over that period of time, the growth rate would be approximately:

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Exponential growth assumes continuous, compounded growth over time. Use logarithms to solve for growth rate r.
Updated On: Feb 20, 2026
  • 1
  • 1.25
  • 1.5
  • 1.75
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The Correct Option is B

Solution and Explanation

  1. The exponential growth rate (r) is determined by the formula:
    \( N_t = N_0 e^{rt} \)
  2. Substituting the values results in: \( 3.2 = 0.4e^{168r} \)
  3. Solving for \( r \) yields approximately \( 0.0125 \) or \( 1.25 \)
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