The rabbit population in a forest area grows at the rate of 5% monthly. If there are 150 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use y=150(2.7)^(0.05t)

To solve this problem, we use the given exponential growth formula:

\[
y = 150 \times (2.7)^{0.05t}
\]

Where:
- \( y \) is the population after \( t \) months.
- \( 150 \) is the initial population in September.
- \( t \) is the time in months after September.

We want to find the population after 12 months (by next September), so we substitute \( t = 12 \) into the equation:

\[
y = 150 \times (2.7)^{0.05 \times 12}
\]

\[
y = 150 \times (2.7)^{0.6}
\]

Next, we calculate \( (2.7)^{0.6} \) and then multiply by 150.

Let's compute this.

\[
y = 150 \times (2.7)^{0.6} \approx 150 \times 1.851
\]

\[
y \approx 277.65
\]

Rounding to the nearest whole number:

\[
y \approx 278
\]

So, by next September, the expected number of rabbits is approximately **278**.

Would you like further details or have any questions?

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Here are 8 related questions:
1. How would the population change if the growth rate increased to 6%?
2. What would be the population after 24 months?
3. How would you modify the equation if the initial population were 200 rabbits?
4. What is the significance of the base \( 2.7 \) in the equation?
5. How does the formula change if we consider yearly growth instead of monthly growth?
6. What is the population after 6 months with the same growth rate?
7. How can we model a decreasing population using a similar formula?
8. What if the growth rate fluctuates monthly? How would that impact the population?

**Tip:** When working with exponential functions, understanding the base and its relation to the growth rate is key to predicting long-term behavior.

Learn how to calculate the expected rabbit population growth using the exponential growth formula. Starting with an initial population of 150 rabbits in September growing at a rate of 5% monthly, find the population expected by next September. Get a step-by-step solution and understand the implications of exponential growth in ecological studies. Suitable for high school students studying growth models.

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