Aaron compared the counts of two species of bacteria after being treated with an antibiotic. The results are shown in the table. Time (hours) & Bacteria 1 Count & Bacteria 2 Count 0 & 6,000 & 8,000 1 & 5,000 & 6,000 2 & 4,500 & 4,500 3 & 4,000 & 3,375 4 & 3,200 & 2,531 Which statement best describes this situation? A. The count of neither of the species is changing exponentially. B. Only the count of bacteria 2 is changing exponentially. C. The counts of both species are changing exponentially. D. Only the count of bacteria 1 is changing exponentially.

## Step 1: Understanding Exponential Change<br />### An exponential change in a quantity occurs when the rate of change is proportional to the current amount. This typically results in a consistent percentage decrease (or increase) over equal time intervals.<br /><br />## Step 2: Analyze Bacteria 1 Count<br />### For Bacteria 1, the counts are decreasing as follows:<br />- From 6,000 to 5,000 (a decrease of 1,000)<br />- From 5,000 to 4,500 (a decrease of 500)<br />- From 4,500 to 4,000 (a decrease of 500)<br />- From 4,000 to 3,200 (a decrease of 800)<br /><br />### The decreases are not consistent in terms of percentage or absolute value, indicating that Bacteria 1 is not changing exponentially.<br /><br />## Step 3: Analyze Bacteria 2 Count<br />### For Bacteria 2, the counts are decreasing as follows:<br />- From 8,000 to 6,000 (a decrease of 2,000)<br />- From 6,000 to 4,500 (a decrease of 1,500)<br />- From 4,500 to 3,375 (a decrease of 1,125)<br />- From 3,375 to 2,531 (a decrease of 844)<br /><br />### The decreases appear to be consistent in terms of percentage, suggesting an exponential decay pattern. To confirm, we can calculate the ratio of consecutive counts:<br />- $\frac{6,000}{8,000} = 0.75$<br />- $\frac{4,500}{6,000} = 0.75$<br />- $\frac{3,375}{4,500} \approx 0.75$<br />- $\frac{2,531}{3,375} \approx 0.75$<br /><br />### Since the ratios are approximately constant, Bacteria 2 is changing exponentially.<br /><br />## Step 4: Conclusion<br />### Based on the analysis, only Bacteria 2 shows an exponential change in count over time.