Question

Noah is growing three different types of trees. He is keeping track of the height of each tree over time.

This equation represents the height (in feet) of the Tree #1 over m months: h=3.5m
The information is in the table is for Tree #2:

time (months) height of tree (feet)
2 5
4 10
5 12.5
8 20
This graph shows how long, in months, it takes Tree #3 to grow h feet.

A graph. Height, in feet. Time, in months.

Which tree is growing the slowest?

Answer 1

Answer:

Tree 3

Step-by-step explanation:

The equation for the height of tree 1 is given as:

h = 3.5m

The equation for the height of tree 2 is gotten using the points from the table (2,5) and (4, 10)

Hence:

$h-h_1=\frac{h_2-h_1}{m_2-m_1}(m-m_1)\\\\h-5=\frac{10-5}{4-2} (m-2)\\\\h-5=2.5m-5\\\\h=2.5m$

From the graph of tree 3, we get the points (2,4) and (4, 8)

Hence:

$h-h_1=\frac{h_2-h_1}{m_2-m_1}(m-m_1)\\\\h-4=\frac{8-4}{4-2} (m-2)\\\\h-4=2m-4\\\\h=2m$

Therefore tree 3 grows the slowest