A tree that is 3 feet tall is growing at a rate of 1 ft per year. A 5 ft tree is growing at a rate of 0.75 ft per year.
The ordered pair (t, h)(t, h) represents the time, t, at height, h.
Which ordered pair represents the year when the trees will be the same height?
A. (6, 9)
B. (8, 11)
C. (7, 10.25)
D. (12, 14)
n: number of years
h1 = h2 = h
3 + n*1 = 5 + n*.75
n = 8 years
3 + 8*1 = 5 + 8*.75 = 11 feet
To determine the year when the trees will be the same height, we need to find the value of t (time) when the heights, h, for both trees are equal.
Let's calculate the height of the first tree after t years:
h1 = 3 + 1t
Next, let's calculate the height of the second tree after t years:
h2 = 5 + 0.75t
To find the year when the trees will be the same height, we need to find the value of t that satisfies the equation h1 = h2.
Setting these equations equal to each other:
3 + 1t = 5 + 0.75t
Simplifying the equation:
0.25t = 2
Dividing both sides of the equation by 0.25:
t = 8
Therefore, the value of t when the trees will be the same height is 8 years.
Thus, the correct ordered pair representing the year when the trees will be the same height is (8, 11).
Therefore, the correct answer is option B: (8, 11).