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To find the population after \( t \) years given an initial population of 3 million and a growth rate of 7% per year, we can use the formula for exponential growth:

\[
P(t) = P_0 \cdot (1 + r)^t
\]

where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population (3 million),
- \( r \) is the growth rate (0.07 for 7%),
- \( t \) is the time in years.

Substituting the values:

\[
P(t) = 3 \cdot (1 + 0.07)^t
\]

Simplify the expression inside the parentheses:

\[
P(t) = 3 \cdot (1.07)^t
\]

So, the population after \( t \) years is given by:

\[
\text{Population} = 3 \cdot (1.07)^t \text{ million}
\]

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Here are some related questions to further understand exponential growth:
1. What happens to the population if the growth rate changes to 5% per year?
2. How would you adjust the formula if the initial population were 5 million instead of 3 million?
3. Can you calculate the population after 10 years using this formula?
4. How does exponential growth compare to linear growth in terms of long-term impact?
5. How would you interpret the result if \( t = 0 \)?

**Tip:** When dealing with exponential growth problems, identify the initial quantity, the growth rate, and apply the formula \( P(t) = P_0 \cdot (1 + r)^t \) for accuracy.

Write an expression representing the given quantity. A population at time t years if it is initially 3 million and growing at 7% per year.

Learn how to model a population growing at 7% per year with an initial size of 3 million. This exponential growth problem uses the formula P(t) = P_0 * (1 + r)^t to represent the population over time.

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