The exponential growth formula is:
$P(t) = P_0 \cdot e^{rt}$ where:

• $P(t)$ is the population at time $t$,
• $P_0$ is the initial population (35,700 in 2005),
• $r$ is the continuous annual growth rate (4% = 0.04),
• $t$ is the time in years from the initial year (2030 - 2005 = 25 years),
• $e$ is the base of the natural logarithm ($\approx 2.718$).

Step-by-Step Calculation:

1. Identify the known values:

   • $P_0 = 35,700$
   • $r = 0.04$
   • $t = 25$

2. Plug the values into the formula: $P(25) = 35,700 \cdot e^{0.04 \cdot 25}$

3. Simplify the exponent: $0.04 \cdot 25 = 1$ So, the equation becomes: $P(25) = 35,700 \cdot e^1$

4. Evaluate $e^1$: $e^1 \approx 2.718$

5. Calculate the population: $P(25) = 35,700 \cdot 2.718 \approx 97,051$

Final Answer:

$97,051$

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Would you like more details or have any questions?
Here are 5 related questions you might find helpful:

1. What happens if the growth rate changes each year?
2. How does continuous growth compare to simple growth?
3. What is the formula for compound interest, and how is it similar to population growth?
4. How does doubling time relate to exponential growth?
5. How can we determine the year when the population will hit 1,000,000?

Tip: Continuous growth models assume that the change occurs infinitely frequently, making them more accurate for biological or economic processes.