/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 4 Suppose a man’s scalp hair gro... [FREE SOLUTION] | 91Ó°ÊÓ

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Suppose a man’s scalp hair grows at a rate of 0.35 mm per day. What is this growth rate in feet per century?

Short Answer

Expert verified
The hair growth rate is 41.9 feet per century.

Step by step solution

01

Convert Millimeters to Feet

First, let's convert the daily growth rate from millimeters to feet. We know that 1 inch is equal to 25.4 millimeters and 1 foot equals 12 inches. Therefore, 1 foot equals 304.8 millimeters. To convert the growth rate of 0.35 mm per day to feet, use the conversion factor: \[\text{Growth rate in feet per day} = \frac{0.35}{304.8}\approx 0.001148936 \text{ feet/day}\]
02

Calculate Annual Growth

Next, calculate how much the hair grows in a single year. There are 365 days in a non-leap year, so: \[\text{Annual growth} = 0.001148936 \times 365 \approx 0.419 feet/year\]
03

Convert Annual Growth to Centurial Growth

To find the hair growth over a century, multiply the annual growth by 100.\[\text{Growth per century} = 0.419 \times 100 = 41.9 \text{ feet/century}\]

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Key Concepts

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

Measurement
Measurement is fundamental to understanding and interpreting the world around us. It involves determining the quantity, size, or extent of something using certain tools or units. In the context of the problem, we are dealing with the measurement of hair growth. This requires us to understand the unit
  • Millimeter (mm)
  • and Foot (ft)
Millimeters are a part of the metric system and are very small units, while feet belong to the imperial system and are larger.
Understanding units is critical when measuring because different contexts may require different units for clarity. For example, when discussing hair growth over time, using millimeters is useful for daily growth, but to express larger amounts like growth over a century, feet may be more appropriate.
Thus, the ability to measure accurately using different units helps us convey meaning effectively in various situations.
Rate Calculation
Rate calculation involves determining how much something changes over a given period. In this exercise, the rate being calculated is the growth of hair over time. Rates are typically expressed using a quantity over time, such as millimeters per day or feet per century.
Calculating rates can be essential for understanding how fast or slow something happens, which is an important aspect in fields like science, economics, and everyday scenarios. This involves multiple steps:
  • Identifying the initial unit rate (e.g., 0.35 mm/day).
  • Converting this rate into another unit system that suits broader analysis (e.g., feet per century).
First, we convert the daily growth rate into a more manageable unit via the conversion factor (from mm to feet), then multiply by the time factor to find the new rate, combining both unit conversion and time expansion.
This thorough understanding of rate calculation helps forecast change over extended periods, making it an invaluable tool in planning and analysis.
Metric Conversion
Metric conversion involves switching between different units of measurement within the metric system, or between metric and other systems like the imperial system. Converting units is crucial for standardization and understanding measurements across different contexts.
To perform a metric conversion, it's important to know the relationship between units. For instance, we know:
  • 1 inch = 25.4 mm
  • 1 foot = 12 inches = 304.8 mm
This exercise asks us to convert 0.35 mm per day into feet per century. By applying these conversion relationships, we calculated that the daily growth rate is approximately 0.001148936 feet per day.
Then, using time conversion principles (i.e., calculating for a century based on annual growth), we arrived at the final growth measurement in a different unit. Being skilled in metric conversion ensures the ability to communicate consistently and correctly in a global context.

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