Given that the population grows exponentially, we can model this situation using the exponential growth formula:

$P = ab^t$

Where:

• $P$ is the population at time $t$,
• $a$ is the initial population (when $t = 0$),
• $b$ is the growth factor per year,
• $t$ is the number of years.

Step-by-step explanation:

1. Initial population: The problem states that the initial population is 18,000 organisms. This is the value of $a$, the starting amount when $t = 0$. $a = 18,000$

2. Growth rate: The population grows by 5.9% per year. To express this as a growth factor $b$, we need to add 1 to the percentage growth rate (since 100% of the population is already there, and 5.9% is added each year): $b = 1 + \frac{5.9}{100} = 1.059$

3. Final model: Now, we can substitute $a = 18,000$ and $b = 1.059$ into the exponential growth formula: $P = 18,000 \times 1.059^t$

Final answer:

The exponential model for the population is:

$P = 18,000 \times 1.059^t$

Would you like further details on how to use this model for specific years or any other questions?

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Here are some related questions for further exploration:

1. How do you calculate the population after 5 years using this model?
2. What is the doubling time for this population?
3. How would the model change if the growth rate was 3% instead of 5.9%?
4. What is the population after 10 years according to the model?
5. How can you graph this exponential model using a tool like Excel or a graphing calculator?

Tip: When working with exponential growth models, always ensure that the growth factor is greater than 1 for growth and less than 1 for decay.