Solve the problem. 14) The rabbit population in a forest area grows at the rate of \( 8 \% \) monthly. If there are 280 rabbits in April, find how many rabbits (rounded to the nearest whole number) should be expected by next April. Use \( y=280(2.7)^{0.08 t} \).

To determine the rabbit population by next April, we'll use the provided growth formula: \[ y = 280 \times (2.7)^{0.08t} \] where: - \( y \) is the expected rabbit population, - \( 280 \) is the initial number of rabbits in April, - \( 2.7 \) is an approximation of Euler's number \( e \) (≈2.71828), - \( 0.08 \) represents the monthly growth rate (8\%), - \( t \) is the time in months. **Step 1: Determine the Time Period** From April to next April is **12 months**. Thus, \( t = 12 \). **Step 2: Substitute the Values into the Formula** \[ y = 280 \times (2.7)^{0.08 \times 12} \] \[ y = 280 \times (2.7)^{0.96} \] **Step 3: Calculate \( (2.7)^{0.96} \)** Using logarithmic and exponential approximations: 1. **Calculate \( \ln(2.7) \):** \[ \ln(2.7) \approx 0.9935 \] 2. **Multiply by the exponent:** \[ 0.9935 \times 0.96 \approx 0.9535 \] 3. **Calculate \( e^{0.9535} \):** \[ e^{0.9535} \approx 2.597 \] **Step 4: Final Calculation** \[ y \approx 280 \times 2.597 \] \[ y \approx 727 \] **Conclusion** By next April, the expected rabbit population is **727 rabbits** (rounded to the nearest whole number). **Answer:** After one year, approximately 727 rabbits are expected by next April.