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. 3. a fellow botanist looks at the log and incorrectly states that the bamboo plant is now $27\frac{1}{2}$ inches taller than it was 25 weeks ago. what is the correct change in the plants height? explain how the error was likely made. the correct change in the plants height is inch(es). the amount trimmed was the growth instead of being the growth.

Explanation:

Step1: Calculate total growth

The plant has grown for 25 weeks at a rate of $\frac{3}{5}$ inch per week. So the total growth is $25\times\frac{3}{5}= 15$ inches.

Step2: Calculate total amount trimmed

Since she trims every 5 weeks and 25 weeks have passed, the number of trimming - sessions is $\frac{25}{5}=5$. Each time she trims $2\frac{1}{2}=\frac{5}{2}$ inches. So the total amount trimmed is $5\times\frac{5}{2}=\frac{25}{2} = 12.5$ inches.

Step3: Calculate net change in height

The net change in height is the total growth minus the total amount trimmed. So it is $15 - 12.5=2.5$ inches.

The error was likely made by adding the amount trimmed to the growth instead of subtracting it.

Answer:

The correct change in the plant's height is $2.5$ inches. The amount trimmed was added to the growth instead of being subtracted from the growth.