Question

a lawncare company developed a new weed killer that is safe to use in vegetable gardens. they applied the weed killer to a vegetable garden that started with 35 weeds. the number of weeds was recorded each day, and it was modeled using the exponential function in the following graph. points a, b, c, and d show how many weeds remained in the garden after 1, 3, 5, and 7 days respectively. which days rate of change would be the best to use in an advertisement for the weed killer? day 1 day 3 day 5 day 7

Explanation:

Step1: Calculate rate of change formula

The rate of change formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate rate of change for Day 1

Initial number of weeds is 35 at $x = 0$. For Day 1 ($x_1=0,y_1 = 35$ and $x_2 = 1,y_2=24.91$), rate of change $=\frac{24.91 - 35}{1-0}=- 10.09$.

Step3: Calculate rate of change for Day 3

For Day 3 ($x_1 = 1,y_1=24.91$ and $x_2 = 3,y_2 = 12.62$), rate of change $=\frac{12.62-24.91}{3 - 1}=\frac{-12.29}{2}=-6.145$.

Step4: Calculate rate of change for Day 5

For Day 5 ($x_1 = 3,y_1=12.62$ and $x_2 = 5,y_2 = 6.4$), rate of change $=\frac{6.4 - 12.62}{5 - 3}=\frac{-6.22}{2}=-3.11$.

Step5: Calculate rate of change for Day 7

For Day 7 ($x_1 = 5,y_1=6.4$ and $x_2 = 7,y_2 = 3.24$), rate of change $=\frac{3.24 - 6.4}{7 - 5}=\frac{-3.16}{2}=-1.58$.

Step6: Compare the absolute - values of rates of change

The absolute - values of the rates of change are: $| - 10.09|=10.09$, $| - 6.145|=6.145$, $| - 3.11|=3.11$, $| - 1.58|=1.58$. The largest absolute - value of the rate of change is for Day 1.

Answer:

A. Day 1