Question

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:

• A. 1
• B. 1.25
• C. 1.5
• D. 1.75

Hint:

Exponential growth assumes continuous, compounded growth over time. Use logarithms to solve for growth rate r.

Answer 1

The Correct Option is B

1. The exponential growth rate (r) can be calculated using the formula:
   \( N_t = N_0 e^{rt} \) 
2. Substituting values: \( 3.2 = 0.4e^{168r} \)
3. Solving for \( r \): \( r \approx 0.0125 \) or \( 1.25 \)