botanist uses the representations below to show the heights in inches, h, of different plants over a period of time, t.
Plant A
Time in weeks, t
60
80
100
120
Height in inches, h
90
120
150
180
Plant B
h = StartFraction 4 t Over 3 EndFraction
A graph has time (in weeks) on the x-axis and height (in inches) on the y-axis. A line goes through points (50, 150) and (120, 360).
If the growth patterns continue, how much taller is the tallest plant than the shortest plant at 120 weeks of growth?
180 inches
200 inches
270 inches
280 inches
To find the height of Plant B at 120 weeks, we can substitute 120 for t in the equation h = (4/3)t:
h = (4/3)(120) = 160 inches
Therefore, at 120 weeks of growth, Plant A has a height of 180 inches and Plant B has a height of 160 inches.
The tallest plant is Plant A, with a height of 180 inches, and the shortest plant is Plant B, with a height of 160 inches.
The difference in height between the tallest and shortest plants at 120 weeks of growth is 180 - 160 = 20 inches.
Therefore, the correct answer is that the tallest plant is 20 inches taller than the shortest plant.
To find out how much taller the tallest plant is than the shortest plant at 120 weeks of growth, we need to determine the heights of each plant at that time.
Let's start with Plant A. From the given representations, we can see that at 120 weeks, the height of Plant A is 180 inches.
For Plant B, we are given the equation h = (4/3)t. Plugging in t = 120 weeks, we have:
h = (4/3)(120)
h = 160 inches
Therefore, at 120 weeks of growth, Plant B is 160 inches tall while Plant A is 180 inches tall.
To find the difference, we subtract the height of Plant B from the height of Plant A:
180 inches - 160 inches = 20 inches
Therefore, the tallest plant is 20 inches taller than the shortest plant at 120 weeks of growth.