To determine the base of the exponential growth model, we can use the following information:

1. The initial population $P_0$ is 202.
2. After one year, the population $P_1$ is 295.

The exponential growth formula is: $P = P_0 \times r^n$ where $r$ is the growth factor per year, and $n$ is the number of years.

Since we know $P_1 = 295$ when $n = 1$, we can set up the equation:

$295 = 202 \times r$

Solving for $r$: $r = \frac{295}{202}$ Calculating this value and rounding to three decimal places:

$r \approx 1.46$

So the completed formula is:

$P = 202 \times (1.46)^n$

Would you like additional details or have any questions?

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Further Questions

1. How does this exponential growth model change if the growth rate decreases over time?
2. What would the population be after 5 years using this model?
3. How would you interpret the growth factor $r = 1.46$ in terms of annual growth rate?
4. What other models besides exponential could represent population growth?
5. How does exponential growth differ from linear growth?

Tip:

When interpreting exponential growth, a growth factor greater than 1 indicates an increase, while a factor less than 1 indicates a decrease over time.