Question

a botanist is studying the development of a bamboo plant. she started keeping a log of its growth 25 weeks ago. since then, the plant has grown an average of $\frac{3}{5}$ inch each week. every 5 weeks she trims $2\frac{1}{2}$ inches off the top of the bamboo plant. its current height is $5\frac{3}{4}$ feet. complete questions 1 - 4 below. (type an integer, fraction, or mixed number.) 2. what is the change in the plants height from being trimmed? 66.5 inch(es) (type an integer, fraction, or mixed number.) enter your answer in the answer box and then click check answer 2 parts remaining

Explanation:

Step1: Determine number of trimming - times

Calculate how many times the plant is trimmed in 25 weeks. Since it's trimmed every 5 weeks, we divide the total number of weeks by 5. So, $25\div5 = 5$ times.

Step2: Calculate total trimming height

Each time $2\frac{1}{2}=\frac{5}{2}$ inches are trimmed. Multiply the number of trimming - times by the amount trimmed each time. So, $5\times\frac{5}{2}=\frac{25}{2}=12.5$ inches. But this is incorrect as we misinterpreted the question. We should note that the change in height from being trimmed is just the total amount trimmed.
The plant is trimmed every 5 weeks for 25 weeks. There are $\frac{25}{5}=5$ trimming - events. Each time $2\frac{1}{2}$ inches are trimmed.
So the total change in height from trimming is $5\times2\frac{1}{2}=5\times\frac{5}{2}=\frac{25}{2} = 12.5$ inches. However, if we assume the 66.5 inches is correct and work backward to check our understanding, we may have misread the question. The correct way is to note that the plant is trimmed 5 times and each trim is $2\frac{1}{2}$ inches.
The total change in height due to trimming is $5\times2\frac{1}{2}=5\times\frac{5}{2}=\frac{25}{2}=12.5$ inches. But if we consider the growth and other factors not relevant to the "change in height from being trimmed" question, we see that the correct way is to just focus on the trimming amount.
The plant is trimmed 5 times with $2\frac{1}{2}$ inches per trim. So the change in height from being trimmed is $5\times2\frac{1}{2}= 12\frac{1}{2}$ inches.

Answer:

$12\frac{1}{2}$