A birch tree that is 4 ft tall grows at a rate of 1 ft per year. A larch tree that is 6 ft tall grows at a rate of 0.5 ft per year.
Let the variable t represent time in years and h represent height in feet. In how many years will the trees be the same height?
Which system of equations can be used to solve this problem?
a.{h=4−t
h=6−0.5t
b.{h=5t
h=6.5t
c.{h=1+4t
h=0.5+6t
d.{h=4+t
h=6+0.5t
b?
Nope. The rate of growth is the slope of the line. Study (D) to see why it is the choice.
No, the correct answer is d. {h=4+t, h=6+0.5t}
To understand why, let's analyze the problem step by step.
We are given that the birch tree grows at a rate of 1 ft per year, so we can express its height, h, as a function of time, t, using the equation:
h = 4 + t
Similarly, the larch tree grows at a rate of 0.5 ft per year, so its height, h, can be represented as:
h = 6 + 0.5t
To find the time when the trees will be the same height, we need to set the heights equal to each other:
4 + t = 6 + 0.5t
Simplifying the equation, we can move all terms involving 't' to one side:
0.5t - t = 6 - 4
-0.5t = 2
Now, divide both sides by -0.5 to isolate 't':
t = 2 / -0.5
Simplifying further, we get:
t = -4
However, since time cannot be negative in this context, we discard this solution.
Therefore, there is no solution in the non-negative time domain, meaning the trees will never be the same height.
No, the correct answer is option a.
The equation for the birch tree's height is h = 4 - t, where t represents time in years.
The equation for the larch tree's height is h = 6 - 0.5t, where t represents time in years.
To find the number of years when the trees will be the same height, we need to solve for t when h for both trees are equal.
Therefore, the correct system of equations is:
h = 4 - t (for the birch tree)
h = 6 - 0.5t (for the larch tree)
Answer: a. {h=4−t, h=6−0.5t}