The given data points suggest how the number of weeds drops over specific days after treatment. Let's analyze these data points:
- Days: [tex]\([2, 4, 6, 8, 10]\)[/tex]
- Number of weeds: [tex]\([100, 26, 6, 2, 1]\)[/tex]
Notice the substantial decrease in the number of weeds at each step. To determine the nature of this rate of change, it's helpful to compare successive values and see if it fits a multiplicative pattern (exponential decay) or an additive pattern (linear decay).
We can examine the ratios between successive values:
- From 100 to 26: [tex]\( \frac{26}{100} = 0.26 \)[/tex]
- From 26 to 6: [tex]\( \frac{6}{26} \approx 0.23 \)[/tex]
- From 6 to 2: [tex]\( \frac{2}{6} \approx 0.33 \)[/tex]
- From 2 to 1: [tex]\( \frac{1}{2} = 0.50 \)[/tex]
These ratios are not exactly the same but show a consistent pattern of significant decrease, indicating the possibility of an exponential decay rather than a linear one. In a linear pattern, the differences between successive values would be roughly constant. However, here the drops are multiplicative, showing each value is a fraction of the previous one.
Thus, the correct conclusion is:
The number of weeds is decreasing by a multiplicative rate.
This means it follows an exponential decay model, where the weed count decreases rapidly over time by a multiplicative factor at each step.
