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. 4. what was the initial height of the plant when the botanist started keeping her log? show your work. the initial height of the plant was inch(es). (type an integer, fraction, or mixed number.) enter your answer in the answer box and then click check answer

Explanation:

Step1: Calculate total growth without trimming

The plant has been growing for 25 weeks at a rate of $\frac{3}{5}$ inch per week. So the total growth without considering trimming is $25\times\frac{3}{5}= 15$ inches.

Step2: Calculate number of trimming - events

Since she trims every 5 weeks and the total time is 25 weeks, the number of trimming - events is $\frac{25}{5}=5$ times.

Step3: Calculate total amount trimmed

Each time she trims $2\frac{1}{2}=\frac{5}{2}$ inches. So the total amount trimmed is $5\times\frac{5}{2}=\frac{25}{2}$ inches.

Step4: Convert current height to inches

The current height is $5\frac{3}{4}$ feet. Since 1 foot = 12 inches, $5\frac{3}{4}$ feet is $5\times12+\frac{3}{4}\times12 = 60 + 9=69$ inches.

Step5: Calculate initial height

Let the initial height be $h$. We know that current height = initial height+total growth - total amount trimmed. So $h=69 - 15+\frac{25}{2}=54+\frac{25}{2}=\frac{108 + 25}{2}=\frac{133}{2}=66\frac{1}{2}$ inches.

Answer:

$66\frac{1}{2}$