/*! 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 7 A person blinks about 9365 times... [FREE SOLUTION] | 91Ó°ÊÓ

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A person blinks about 9365 times a day. Each blink lasts about \(0.15\) second. If one person lives 72 years, how many years will be spent with his or her eyes closed while blinking? Write your answer in scientific notation.

Short Answer

Expert verified
Around 1.171 years.

Step by step solution

01

Calculate Total Seconds Blinking Per Day

To find the total seconds spent blinking in one day, multiply the number of blinks per day by the duration of each blink. \[ 9365 \text{ blinks/day} \times 0.15 \text{ seconds/blink} = 1404.75 \text{ seconds/day} \]
02

Convert Seconds to Minutes Per Day

To convert total seconds spent blinking per day into minutes, divide the total seconds by 60.\[ \frac{1404.75 \text{ seconds}}{60 \text{ seconds/minute}} = 23.4125 \text{ minutes/day} \]
03

Convert Minutes to Hours Per Day

To convert the blinking time per day from minutes to hours, divide the total minutes by 60.\[ \frac{23.4125 \text{ minutes}}{60 \text{ minutes/hour}} = 0.3902083 \text{ hours/day} \]
04

Calculate Total Hours Blinking Per Year

To find the total hours spent blinking in a year, multiply the daily blinking hours by the days in a year.\[ 0.3902083 \text{ hours/day} \times 365 \text{ days/year} = 142.38502 \text{ hours/year} \]
05

Convert Hours to Days Per Year

To convert total hours per year to days, divide by 24.\[ \frac{142.38502 \text{ hours/year}}{24 \text{ hours/day}} = 5.9327 \text{ days/year} \]
06

Calculate Total Days Blinking Over a Lifetime

Multiply the blinking days per year by the total number of years lived (72).\[ 5.9327 \text{ days/year} \times 72 \text{ years} = 427.1504 \text{ days} \]
07

Convert Days to Years

Convert the total blinking days into years by dividing by 365.\[ \frac{427.1504 \text{ days}}{365 \text{ days/year}} \approx 1.1707 \text{ years} \]
08

Express in Scientific Notation

Express the calculated years in scientific notation.\[ 1.1707 \text{ years} \approx 1.171 \times 10^0 \text{ years} \]
09

Conclusion

The total time spent blinking over a 72-year lifetime is approximately 1.171 years.

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Key Concepts

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

time calculation
When calculating time, it's essential to break it down into digestible parts. For instance, in this problem, we start by determining how much time is spent on an activity each day. It's wise first to find out how much time in seconds, minutes, and then hours is dedicated to an activity each day. In our blinking exercise, we begin by calculating the time taken in seconds:
  • With 9365 blinks in a day, and each blink taking 0.15 seconds, this results in 1404.75 seconds per day spent blinking.
When you have a daily total in seconds, converting it to minutes involves dividing by 60, since there are 60 seconds in a minute. This gives us 23.4125 minutes per day.
Next, to get hours from minutes, divide by 60 again, leading to approximately 0.3902 hours per day spent blinking. It's all about step-by-step conversions, ensuring you use the right factor for each unit transition.
lifetime estimation
Lifetime estimation involves projecting an activity's daily occurrence over a human lifespan. In this case, the blinking hours per day is extrapolated over a year and then a lifetime:
  • Once you know how many hours a day are spent blinking (around 0.3902 hours), multiply by 365 to find the hours spent per year: 142.385 hours.
Now, you can convert this annual amount into days by dividing by 24, the number of hours in a day, resulting in about 5.9327 days a year.
Next, to see how much time is spent blinking over a lifetime, multiply the days per year by the expected lifetime. In this exercise, this is 72 years, which yields approximately 427.15 total days.
This cumulative approach over one's life allows us to understand how small daily actions add up to significant amounts over many years.
unit conversion
Unit conversion is the backbone of translating numbers from one measure to another accurately. In real-world applications, including scientific contexts, properly converting units ensures precision. Here's how:
  • Start with a known quantity. For example, seconds to minutes is converting using the factor 60 (since 60 seconds = 1 minute).
  • For minutes to hours, again use 60, given 60 minutes make an hour. Then for hours to days, use 24 since 24 hours equal a day.
After these conversions, for our blinking exercise, converting the lifetime blinking days to years involves using 365 days for every year.
At the end, expressing the results in scientific notation can simplify high-value numbers, facilitating easier interpretation and communication across scientific platforms. Whether dealing with time, weight, volume, or any other measure, these unit shifts are indispensable in analysis and calculation.

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