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Chapter 1: Problem 12

The fastest growing plant on record is a Hesperoyucca whipplei that grew \(3.7 \mathrm{~m}\) in 14 days. What was its growth rate in micrometers per second?

Short Answer

Expert verified
The growth rate is approximately 3.06 micrometers per second.

Step by step solution

01

Convert growth from meters to micrometers

Start by converting the total growth of the plant from meters to micrometers. There are \(10^6\) micrometers in a meter, so:\[3.7 \text{ m} = 3.7 \times 10^6 \text{ micrometers}.\]
02

Convert time from days to seconds

Next, convert the time duration from days to seconds. There are 86400 seconds in a day, so:\[14 \text{ days} = 14 \times 86400 \text{ seconds}.\]
03

Calculate the growth rate in micrometers per second

Now calculate the growth rate using the formula:\[\text{growth rate} = \frac{\text{total growth in micrometers}}{\text{total time in seconds}}.\]So, substitute the values:\[\text{growth rate} = \frac{3.7 \times 10^6}{14 \times 86400}.\]
04

Simplify to get the growth rate

Perform the calculation from Step 3:1. Calculate \(14 \times 86400 = 1209600\).2. Divide \(3.7 \times 10^6\) by 1209600:\[\text{growth rate} \approx 3.06 \text{ micrometers per second}.\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Units Conversion
Understanding units conversion is essential in science and daily living. It allows us to interpret measurements accurately across different scales and units. In this exercise, we have a growth of 3.7 meters, which needs to be converted into micrometers. To convert meters to micrometers, remember that 1 meter equals 1,000,000 micrometers. This is
  • Meter to micrometer: Multiply the meter value by \(10^6\).
Following this method, you calculate the plant's growth to be 3.7 meters, which is equivalent to \(3.7 \times 10^6\) micrometers. Breaking down units like this makes it easier to handle large or small numbers in various physics problems, enabling precise calculations for any conversions you come across.
Growth Rate Calculation
Calculating growth rate is a meaningful skill that helps us understand how quickly or slowly something changes over time. Think of the growth rate as the speed at which growth occurs over a specified period. To find the growth rate, we divide the total growth by the total time taken for that growth.
  • Total growth: Measured in micrometers after conversion.
  • Total time: Measured in seconds after conversion.
The formula applied here is: \[\text{Growth rate} = \frac{\text{Total growth}}{\text{Total time in seconds}}\]By substituting the values given in the problem, you arrive at the final growth rate in terms of micrometers per second. This simple division allows you to comprehend the problem's overall requirements, ensuring you accurately assess the situation based on transformed given data.
Micrometers per Second
Expressing a growth rate in micrometers per second is a common way to convey small but significant changes over time. When you break down the problem, you translate large outputs like meters and days into micrometers and seconds, making the results more intuitive within the context of the problem.Here's how the values play out:
  • Growth in micrometers: Clearly calculated as \(3.7 \times 10^6\).
  • Time in seconds: Detailed calculation results in 1,209,600 seconds.
By performing the division, you achieve a growth rate of approximately 3.06 micrometers per second. This unit of measurement helps visualize compact growth rates, enabling easy comparison across different phenomena, ensuring precision in scientific research or any life-scale application requiring such refined measurements.

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Most popular questions from this chapter

(a) A unit of time sometimes used in microscopic physics is the shake. One shake equals \(10^{-8} \mathrm{~s}\). Are there more shakes in a second than there are seconds in a year? (b) Humans have existed for about \(10^{6}\) years, whereas the universe is about \(10^{10}\) years old. If the age of the universe is defined as 1 "universe day," where a universe day consists of "universe seconds" as a normal day consists of normal seconds, how many universe seconds have humans existed?

In the United States, a doll house has the scale of 1: 12 of a real house (that is, each length of the doll house is \(\frac{1}{12}\) that of the real house and a miniature house (a doll house to fit within a doll house ) has the scale of 1: 144 of a real house. Suppose a real house (Fig. \(1-7)\) has a front length of \(20 \mathrm{~m},\) a depth of \(12 \mathrm{~m},\) a height of \(6.0 \mathrm{~m}\) and a standard sloped roof (vertical triangular faces on the ends) of height \(3.0 \mathrm{~m} .\) In cubic meters, what are the volumes of the corresponding (a) doll house and (b) miniature house?

Water is poured into a container that has a small leak. The mass \(m\) of the water is given as a function of time \(t\) by \(m=5.00 t^{0.8}-3.00 t+20.00,\) with \(t \geq 0, m\) in grams, and \(t\) in seconds. (a) At what time is the water mass greatest, and (b) what is that greatest mass? In kilograms per minute, what is the rate of mass change at \((\mathrm{c}) t=2.00 \mathrm{~s}\) and (d) \(t=5.00 \mathrm{~s} ?\)

A typical sugar cube has an edge length of \(1 \mathrm{~cm} .\) If you had a cubical box that contained a mole of sugar cubes, what would its edge length be? (One mole \(=6.02 \times 10^{23}\) units.)

Two types of barrel units were in use in the \(1920 \mathrm{~s}\) in the United States. The apple barrel had a legally set volume of 7056 cubic inches; the cranberry barrel, 5826 cubic inches. If a merchant sells 20 cranberry barrels of goods to a customer who thinks he is receiving apple barrels, what is the discrepancy in the shipment volume in liters?
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