This problem involves exponential growth, where the population doubles every 9 years under ideal conditions. Let's break it down step-by-step.

Step 1: General formula for exponential growth

The population of a species that grows exponentially can be modeled by the formula: $P(t) = P_0 \cdot 2^{\frac{t}{T}}$ where:

• $P_0$ is the initial population,
• $T$ is the time it takes for the population to double,
• $t$ is the elapsed time,
• $P(t)$ is the population after $t$ years.

Step 2: Input the given values

From the problem:

• $P_0 = 100$ (initial population),
• $T = 9$ years (time to double).

Substitute these into the general formula: $P(t) = 100 \cdot 2^{\frac{t}{9}}$

Step 3: Final expression

The expression for the population $t$ years after the start is: $P(t) = 100 \cdot 2^{\frac{t}{9}}$

This formula represents the population under ideal conditions, where it doubles every 9 years.

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Related Questions:

1. How would the formula change if the population doubled every 5 years instead?
2. What is the population after 27 years using the given formula?
3. How long will it take for the population to reach 800 individuals?
4. Can this formula be used to model human population growth, or are other factors involved?
5. How does exponential growth differ from linear growth?

Tip:

When working with exponential growth, always check the doubling time and ensure it matches the given conditions!