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}`

Step-by-step 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}=(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}=(y_2-y_1)/(x_2-x_1) \\ slope_1=(13.5-9)/(6-4)=(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}=(y_2-y_1)/(x_2-x_1) \\ \text{slope}=(20.25-13.5)/(9-6)=(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