Question

plant a
in science, students are observing the growth of two plants.
plant a receives sunlight and plant b does not. the graph
and table show the data for this scenario.
what is the initial height of plant b?
3 inches

Explanation:

Step1: Understand the concept of initial height

The initial height of a plant (in the context of a time - height relationship) is the height of the plant at time \(x = 0\). For a linear relationship (which can be represented by a table or a graph), if we assume the relationship is of the form \(y=mx + b\) (where \(y\) is height, \(x\) is time, \(m\) is the slope, and \(b\) is the \(y\) - intercept), the \(y\) - intercept \(b\) gives the value of \(y\) when \(x = 0\).

Step2: Analyze the table for Plant B

Looking at the table for Plant B, when \(x = 0\) (initial time, weeks = 0), we can use the pattern of the data. If we assume a linear relationship. Let's check the rate of change (slope) first. For two points \((x_1,y_1)=(1,7.3)\) and \((x_2,y_2)=(2,8.2)\) (assuming the table data: if \(x = 1,y = 7.3\) and \(x = 2,y = 8.2\)), the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{8.2-7.3}{2 - 1}=0.9\).
Using the point - slope form \(y - y_1=m(x - x_1)\), with \(x_1 = 1,y_1 = 7.3\) and \(m = 0.9\), we have \(y-7.3=0.9(x - 1)\).
When \(x = 0\), \(y-7.3=0.9(0 - 1)\), \(y=7.3-0.9=6.4\)

Answer:

The initial height of Plant B is \(6.4\) inches.