Question

Time(wki469Height ofplant (in)9.013.520.25Find the rate of change for weeks 40le and 69.Explain the meaning of the rate of change for each case.

Answer 1

$\begin{gathered} slope_1=slope_2=2.25 \\ \end{gathered}$

Explanation

Step 1

when you have 2 coordinates ( A and B), the slope of the line that passes thought those point is given by

$\text{slope}=\frac{y_2-y_1}{x_2-x_1}$

where

$\begin{gathered} A=(x_1,y_1) \\ B=(x_2,y_2) \end{gathered}$

A and B are 2 known points of the line

Step 2

so, the slope represents the rate of change

i)the rate of change for 4-6 weeks

Let

A=(4 ,9)

B=(6,13.5)

replace

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope_1=\frac{13.5-9}{6-4}=\frac{4.5}{2}=2.25 \\ slope_1=2.25 \end{gathered}$

Step 3

ii)the rate of change for 6-9weeks

Let

A(6,13.5)

B(9,20.25)

replace,

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{20.25-13.5}{9-6}=\frac{6.75}{3}=2.25 \end{gathered}$

the slope represents the rate of change, it means for every case the plant is growing at a constant rate (2.25 inches per week)

I hope this helps you