Question

Determining the Effect of a New Rate of Change
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.

Assume Plant B received sunlight, and its rate of change was 1.6 inches a week instead of 1.4 inches per week. Would it be taller at 6 weeks?
No. It will be shorter.
No. It will be the same height.
Yes. It will be 0.3 inches taller.
Yes. It will be 4.5 inches taller.

Answer 1

Yes. It will be 0.3 inches taller.

Work:
- Plant A: height = 3 + 1.8t, so at t = 6 → 3 + 1.8(6) = 13.8 in.
- Plant B (with new rate 1.6): from table m = 1.4 and b = 7.3 − 1.4(2) = 4.5, so with m = 1.6 new height = 4.5 + 1.6(6) = 14.1 in.

14.1 − 13.8 = 0.3 in taller.