Question

1. Application:

The equation below give the heights y, and y₂ (in inches) of two bamboo plants over a period of 30 days,
where x represents the time in days.
Plant 1: y₁ = 2x + 50,0 ≤ x ≤ 30
Plant 2: y₂ = 4x + 20, 0≤x≤ 30
a. Explain how you can use the equations to determine the heights of the plants on Day 0.
b. Which plant grew at a faster rate? Explain.
C.
Were the two plants ever the same height? Explain

Answer 1

To determine the heights of the plants on Day 0, substitute x = 0 into the equations. Plant 2 grew at a faster rate based on the coefficient of x in the equations. The two plants were never the same height within the given time range.

Step-by-step explanation:

a. To determine the heights of the plants on Day 0, we need to substitute x = 0 into the equations.

For Plant 1:

y₁ = 2(0) + 50 = 50 inches

For Plant 2:

y₂ = 4(0) + 20 = 20 inches

Therefore, on Day 0, Plant 1 height is 50 inches and Plant 2 height is 20 inches.

b. To determine which plant grew at a faster rate, we can compare the coefficients of x in the equations. The coefficient of x in Plant 1 is 2, while the coefficient of x in Plant 2 is 4. Since 4 > 2, Plant 2 grew at a faster rate.

c. The two plants were never the same height. This can be seen by solving the equations for when the heights y₁ and y₂ are equal:

2x + 50 = 4x + 20
50 - 20 = 4x - 2x
30 = 2x
x = 15

Since x = 15, it means the two plants would have the same height after 15 days. However, the given time period is 0 to 30 days, so they were never the same height within this range.

Learn more about Calculating heights and growth rates of bamboo plants