Question

The fastest growing plant on record is a Hesperoyucca whipplei that grew 3.7 m in 14 days. What was its growth rate in micrometers per second?

Answer 1

The growth rate of a plant is equal to the increase in size of the plant per unit time. We are given the length of the plant after 14 days from which we can calculate the required rate by converting various units to micrometers and second then dividing the length with time.

Complete step by step answer:
We are given that a Hesperoyucca whipplei, which is the fastest growing plant on record, grows to a length of 3.7 m in the duration of 14 days.
We need to calculate the rate of growth of the plant in units of micrometers per second.
The rate of the growth of the plant can be defined as the ratio of the increase in length of the plant to the total time taken to reach that length.
First, we need to convert the units of length which are given in meters into micrometers. We know for this unit of length that
$1\mu m = {10^{ - 6}}m \\\ \Rightarrow 1m = {10^6}\mu m \\\$
Also in case of unit of time, one day can be converted into seconds by the following relation:
$1{\text{ day}} = 24hr = 24 \times 60\min = 24 \times 60 \times 60s$
Now we can finally calculate the rate of growth of a Hesperoyucca whipplei which can be done by dividing the increase in length of plant with the time taken for the growth by the same amount.
Rate $= \dfrac{{3.7m}}{{14{\text{ days}}}}$
Now we will use the various conversions for units obtained above. Doing so we get the rate as
Rate $= \dfrac{{3.7 \times {{10}^6}\mu m}}{{14 \times 24 \times 60 \times 60s}} = 3.058\mu m/s$
This is the required answer.

Note: We study the rates of change of natural phenomena like the growth of plants because rate signifies the increase that takes place every second. It plays an important role in understanding many natural and physical phenomena.