1. **Problem statement:** A jar starts with 1000 g of sugar. Each day, half of the sugar present is removed. We want to find how much sugar remains after 5 days. 2. **Formula:** The amount of sugar left after $n$ days is given by the exponential decay formula: $$\text{Sugar_left} = 1000 \times \left(\frac{1}{2}\right)^n$$ where $n$ is the number of days. 3. **Calculate sugar left after 5 days:** $$\text{Sugar_left} = 1000 \times \left(\frac{1}{2}\right)^5$$ 4. Simplify the exponent: $$\left(\frac{1}{2}\right)^5 = \frac{1}{2^5} = \frac{1}{32}$$ 5. Substitute back: $$\text{Sugar_left} = 1000 \times \frac{1}{32}$$ 6. Multiply: $$\text{Sugar_left} = \frac{1000}{32} = 31.25$$ 7. **Answer for part (a):** At the end of the 5th day, there will be 31.25 g of sugar left in the jar. 8. **Part (b) explanation:** Since each day the sugar amount is halved, it approaches zero but never actually reaches zero. This is because halving a positive number repeatedly gets smaller and smaller but never becomes exactly zero. **Final answers:** - (a) 31.25 g - (b) The jar will never be completely empty, but the sugar amount will get closer and closer to zero over time.