To find the population after 12 years given a 3% annual growth rate, we can use the formula for compound interest:

$P(t) = P_0 \times (1 + r)^t$

Where:

• $P(t)$ is the population after $t$ years.
• $P_0$ is the initial population.
• $r$ is the growth rate per period (in decimal form).
• $t$ is the number of years.

Given:

• $P_0 = 400,000$
• $r = 0.03$ (3% growth rate)
• $t = 12$ years

Plugging in the values:

$P(12) = 400,000 \times (1 + 0.03)^{12}$

$P(12) = 400,000 \times (1.03)^{12}$

Now, let's calculate this:

$P(12) \approx 400,000 \times 1.42576 \approx 570,304$

So, the population after 12 years will be approximately 570,304 people.

Would you like more details or have any questions?

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Here are 5 related questions:

1. How would the population change if the growth rate were 5% instead of 3%?
2. What would be the population after 20 years with the same 3% growth rate?
3. How can we adjust the formula if the population were to decrease by 2% annually?
4. What is the population doubling time given a 3% growth rate?
5. How does the compound interest formula apply to financial investments?

Tip: When dealing with exponential growth, small changes in the rate can lead to significant differences over time.