Question

Plant A: A graph has time (weeks) on the x-axis, and height (inches) on the y-axis. A line goes through points (0, 3), (1, 4.8), (2, 6.6), (3, 8.4). Plant B: A 2-column table with 3 rows. Column 1 is labeled Weeks with entries 2, 3, 4. Column 2 is labeled Height (inches) with entries 7.3, 8.7, 10.1. Simon claims that Plant B will be taller than Plant A in 6 weeks because it has the greater initial value. Is he correct? Yes. The plant with the greater initial value will continue to be taller. Yes. Plant B is 2.4 inches taller than Plant A at 6 weeks. No. The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks. No. The initial value of Plant A is greater.

Answer 1

No. The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks.

Explanation:

Answer 2

The correct option is;

No, The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks

Explanation:

The parameters given are;

Plant A:

Weeks, Height

0, 3

1, 4.8

2, 6.6

3, 8.4

The rate of change of height, H per week, t,
`\left ((dH)/(dt) \right )` for plant A per week is therefore;

`(dH)/(dt) = (H_n - H_((n-1)) )/(t_n - t_((n-1))) = (8.4 - 3 )/(3 - 0) = (5.4)/(3) = 1.8 \ inches/week`

Therefore we have;

H = 1.8 × t + 3

At week 6,

H = 3 + 6×1.8 = 13.8 inches

Plant B

Weeks, Height

2, 7.3

3, 8.7

4, 10.1

The rate of change of height, H per week, t,
`\left ((dH)/(dt) \right )` for plant B per week is given as follows;

`(dH)/(dt) = (H_n - H_((n-1)) )/(t_n - t_((n-1))) = (10.1 - 7.3 )/(4 - 2) = (2.8)/(2) = 1.4 \ inches/week`

Therefore we have;

When t = 2, H = 7.3 hence, 7.3 = 2 × 1.4 + H₀

Where:

H₀ = H at t = 0

H₀ = 7.3 - 2 × 1.4 = 4.5

At week 6 we have;

H = 4.5 + 6×1.4 = 12.9 inches

Which indicates that Plant A will be 0.9 inches taller than Plant B at week 6.

The correct option is therefore;

No, The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks.