The rabbit population in a forest area grows at the rate of 8% monthly. If there are 230 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use y=230(2.7)^(0.08t)

To solve this problem using the provided formula:

\[
y = 230 \times (2.7)^{0.08t}
\]

Where:
- \( y \) is the population after \( t \) months.
- \( 230 \) is the initial population in September.
- \( t \) is the time in months after September.
- The growth rate is 8% per month.

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

\[
y = 230 \times (2.7)^{0.08 \times 12}
\]

\[
y = 230 \times (2.7)^{0.96}
\]

Next, we calculate \( (2.7)^{0.96} \) and then multiply by 230.

Let's compute this:

\[
y = 230 \times (2.7)^{0.96} \approx 230 \times 2.421
\]

\[
y \approx 556.83
\]

Rounding to the nearest whole number:

\[
y \approx 557
\]

So, by next September, the expected number of rabbits is approximately **557**.

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 10%?
2. What would be the population after 6 months with an 8% growth rate?
3. How would you modify the equation if the initial population were 300 rabbits?
4. What is the significance of the exponent \( 0.08t \) in the equation?
5. How does the formula change if we consider a different base instead of \( 2.7 \)?
6. What if the growth rate decreases over time? How would that affect the population?
7. How can this model be adapted for predicting populations over a longer period, like 5 years?
8. What if the initial population was lower, say 150 rabbits, but the growth rate was 12%?

**Tip:** Exponential growth can lead to rapid increases in populations, so it's essential to understand how small changes in the growth rate or time period can have significant impacts.

Learn how to predict rabbit population growth using the exponential growth formula y = 230 * (2.7)^(0.08t). Understand how changes in growth rate affect population predictions. Calculate expected rabbit population by next September starting from 230 rabbits in September.

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