A population grows according to an exponential growth model. The initial population is 202 and the population after one year is 295.
Complete the formula where P is the population and n is the number of years.:
P=202*(__)^n
Round your answer to three decimal places.

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.

A population grows according to an exponential growth model. The initial population is 202 and the population after one year is 295. Complete the formula where P is the population and n is the number of years: P=202*(__)^n. Round your answer to three decimal places.

Explore how to determine the growth rate in an exponential population model where the initial population is 202 and grows to 295 after one year. This problem covers exponential growth concepts, population modeling, and algebra, ideal for students in Grades 9-11.

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