Answer:
18 days
Step-by-step explanation:
Here's a short table of heights:
day 0: height = 1
day 1: height = 1 + (1/2)(1) = 3/2
day 2: height = (3/2) + (1/3)(3/2) = 3/2 + 1/2 = 2
The pattern of heights is ...
(day, height) = (0, 1), (1, 1.5), (2, 2)
The plant is growing 1/2 its original height each day, so we can write the equation ...
h = 1 + d/2
We want to find the number of days (d) that result in a height of 10 (ten times the original height).
10 = 1 + d/2
9 = d/2 . . . . subtract 1
18 = d . . . . . multiply by 2
It took 18 days for the plant to grow to 10 times its original height.
