Final answer:
To calculate the expected rabbit population after one year with a monthly growth of 5%, apply the formula y = 150(2.7)^(0.05t) with t=12 months, compute the result, and round to the nearest whole number.
Step-by-step explanation:
The question involves calculating the expected population of rabbits in a forest area after one year, given an initial population and a monthly growth rate. To find how many rabbits should be expected by next September from an initial population of 150 rabbits growing at a 5% monthly rate, we use the formula y = 150(2.7)^(0.05t), where t is the time in months.
- First, identify the time period: since we are looking at the growth from one September to the next, t = 12 months.
- Next, plug the value of t into the formula: y = 150(2.7)^(0.05*12).
- Calculate the exponent: 0.05*12 = 0.6 and then compute 2.7^0.6.
- Finally, multiply this result by 150 to find the expected population after one year.
The final calculation will provide us with the projected number of rabbits, which we then round to the nearest whole number as per the question's instructions. As this math involves exponential growth, it highlights how the population can rapidly increase over time when subjected to a consistent growth rate.