Question

lawn care
lawn care
based on the graph of the regression model, which is true?
the number of weeds is decreasing by a multiplicative rate.
the number of weeds is increasing by a multiplicative rate.
the number of weeds is decreasing by an additive rate.
the number of weeds is increasing by an additive rate.

Explanation:

Step1: Analyze the trend of the graph

The graph shows that as the number of days after treatment ($x$) increases, the number of weeds ($y$) decreases. So we can eliminate the options where the number of weeds is increasing (options 2 and 4).

Step2: Determine the rate of decrease

An additive rate of decrease would mean a constant change in the number of weeds per day (a linear relationship). A multiplicative rate of decrease would mean that the number of weeds is multiplied by a constant factor each day (an exponential relationship). The graph is a curve, not a straight - line. For a straight - line (linear) relationship (additive rate), the equation is of the form $y=mx + b$. For an exponential relationship (multiplicative rate), the equation is of the form $y = a\cdot r^{x}$. Since the graph is not a straight - line, it is not an additive rate.

Answer:

The number of weeds is decreasing by a multiplicative rate.