1. **Problem Statement:** A baby chicken weighs 32 grams at hatching (week 0). Its mass increases by 45% each week for 12 weeks. We need to complete the table showing the chicken's mass over time. 2. **Formula:** The mass after $n$ weeks is given by the formula for exponential growth: $$ M_n = M_0 \times (1 + r)^n $$ where: - $M_0 = 32$ grams (initial mass), - $r = 0.45$ (45% increase per week), - $n$ is the number of weeks. 3. **Calculate mass for week 1:** $$ M_1 = 32 \times (1 + 0.45)^1 = 32 \times 1.45 = 46.4 $$ (Note: The user wrote 76.40, which seems incorrect for 45% increase from 32.) 4. **Calculate mass for week 2:** $$ M_2 = 32 \times 1.45^2 = 32 \times 2.1025 = 67.28 $$ 5. **Calculate mass for week 3:** $$ M_3 = 32 \times 1.45^3 = 32 \times 3.0486 = 97.56 $$ 6. **General calculation:** For each week $n$ from 0 to 12, calculate: $$ M_n = 32 \times 1.45^n $$ 7. **Summary table (rounded to two decimals):** | Week | Mass (g) | |-------|----------| | 0 | 32.00 | | 1 | 46.40 | | 2 | 67.28 | | 3 | 97.56 | | 4 | 141.46 | | 5 | 205.07 | | 6 | 297.37 | | 7 | 430.42 | | 8 | 623.11 | | 9 | 903.51 | | 10 | 1309.08 | | 11 | 1898.17 | | 12 | 2752.34 | **Note:** The mass grows quickly due to the 45% weekly increase. --- **Reflection on problems 9-12:** - $3^3 = 27$ (not 9 as stated) - $2(3^3) = 2 \times 27 = 54$ - $3^3 + 4 = 27 + 4 = 31$ - $2 \cdot 3^3 + 4 = 2 \times 27 + 4 = 54 + 4 = 58$ --- **Answer to #8:** To find the mass at week 1, multiply the initial mass by 1.45 (which is 100% + 45%). Then for week 2, multiply the week 1 mass again by 1.45, and so on. This is exponential growth, not just adding 45% of 32 each week.