Question

amir is growing three plants.
he keeps track of each plant’s height over time.
which plant is growing the slowest?
plant 1 plant 2 plant 3
plant 1
height (in)
time (months)
plant 2
time (months) height (in.)
2 5
4 10
6 15
8 20
10 25
plant 3
$h = 3.5t$
t time (months)
h height (in.)

Explanation:

Step1: Find slope of Plant 1

From the graph, at \( t = 2 \), \( h = 4 \); at \( t = 4 \), \( h = 8 \). Slope \( m_1=\frac{8 - 4}{4 - 2}=\frac{4}{2}=2 \) inches per month.

Step2: Find slope of Plant 2

From the table, at \( t = 2 \), \( h = 5 \); at \( t = 4 \), \( h = 10 \). Slope \( m_2=\frac{10 - 5}{4 - 2}=\frac{5}{2}=2.5 \) inches per month.

Step3: Find slope of Plant 3

From the equation \( h = 3.5t \), the slope \( m_3 = 3.5 \) inches per month.

Step4: Compare slopes

\( m_1 = 2 \), \( m_2 = 2.5 \), \( m_3 = 3.5 \). The smallest slope is \( m_1 \), so Plant 1 grows slowest.

Answer:

Plant 1