1. **State the problem:** We have a sugar concentration in blood that decreases by the same factor every hour. Given the concentrations at times 0, 1, 2, and 3 hours, we want to find: a) The factor by which the concentration is multiplied each hour. b) The percentage decrease in concentration each hour. 2. **Identify the formula:** This is an example of exponential decay, where the concentration $C$ at time $t$ is given by: $$C_t = C_0 \times r^t$$ Here, $C_0$ is the initial concentration, $r$ is the decay factor per hour (a number between 0 and 1), and $t$ is time in hours. 3. **Find the decay factor $r$:** Using the data at $t=0$ and $t=1$: $$C_1 = C_0 \times r$$ Substitute values: $$160 = 200 \times r$$ Divide both sides by 200: $$\frac{160}{200} = \cancel{\frac{200}{200}} \times r \Rightarrow 0.8 = r$$ So, the concentration is multiplied by $0.8$ each hour. 4. **Verify with other data points:** For $t=2$: $$C_2 = 200 \times 0.8^2 = 200 \times 0.64 = 128$$ Matches the table. For $t=3$: $$C_3 = 200 \times 0.8^3 = 200 \times 0.512 = 102.4$$ Matches the table. 5. **Calculate the percentage decrease:** Since the concentration is multiplied by $0.8$ each hour, the decrease is: $$100\% - 80\% = 20\%$$ So, the concentration decreases by 20% each hour. **Final answers:** - a) The concentration is multiplied by $0.8$ each hour. - b) The concentration decreases by 20% each hour.