Nails take between 12 and 18 months to regrow completely. They grow at an average rate of 3 mm/month, r = 0.003 m/month

Assumptions:

• The mean length of time for a nail to regrow is 15 months
• The average fingernail length from cuticle to fingertip is 20 mm - 0.02 m
• Ten fingers from birth to death
• Average life expectancy, despite gender and other circumstances, is 78 years / 936 months

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There is a maximum length for fingernails from birth to death that can be acquired. This is calculated as r x (average life expectancy). 0.003 m/month x 936 months = 2.808 m.

US population has increased relatively linearly since 1940 from ~130 million to ~320 million. Average crude death rate since 1940 is 0.9679%. Furthermore, as the US population ages, the age-adjusted death rate drops by approximately 0.0143% per year.

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So first lets assume every person reaches age 78, and when they die, their fingernail length is 0.02 m. This means that the rest (2.808 m - 0.02 m = 2.788 m) is in the landfill (per your assumption). We now add the combined lengths of fingernails for each year group together (Month, Length) :

• { (1, 0.003), (2, 0.006), ... (934, 2.802), (935, 2.805), (936, 2.788) }

To do this, we need the age distribution. The most precise info I could find all cites the CIA World Factbook. We have ages 0-14 representing 19.4% of population, 15-24 is 13.7%, 25-54 is 39.9%, 55-64 is 12.6%, and 65+ is 13.9%. Since we are assuming everyone makes it to age 78, and the current population is 320 million, we can create a group (Age Group (Years), Population (in millions)).

• { (0-14, 62.08), (15-24, 43.84), (24-54, 127.68), (55-64, 40.32), (65 - 78, 44.48) }

Since we currently have the same mortality rate across the board, we can distribute the second value of each pair evenly across the age group measured, i.e. (0-14, 62.08) --> 62.08/15 ~= 4.139 per year group. Then we divide this by 12 to get the population per month - 4.139/12 = 0.345 million people per month. We will now create a group for this data ( Age Group (Years), People per Month (millions) ):

• { (0-14, 0.345), (15-24, 0.365), (25-54, 0.355), (55-64, 0.336), (65-78, 0.265) }

We can now match these up with the (Month, Length) data to obtain cumulative fingernail length in landfill.

• (1, 0.345 x 0.003), (2, 0.345 x 0.006), ..., (178, 0.345 x 0.534), (179, 0.345 x 0.537)
• (180, 0.365 x 0.54), (181, 0.365 x 0.543), ..., (298, 0.365 x 0.894), (299, 0.365, 0.897)
• (300, 0.355 x 0.9), (301, 0.355 x 0.903), ..., (658, 0.355 x 1.974), (659, 0.355 x 1.977)
• (660, 0.336 x 1.98), (661, 0.336 x 1.983), ..., (768, 0.336 x 2.304), (769, 0.336 x 2.307)
• (770, 0.265 x 2.31), (771, 0.265 x 2.313), ..., (946, 0.265 x 2.838), (947, 0.265 x 2.841)

becomes

• sum i = 1 to 179 : 0.345 x (0.003 x i) = 0.001035 x i = 16.67385 million m
• sum i = 180 to 299 : 0.365 x (0.003 x i) = 0.001095 x i = 31.4703 million m
• sum i = 300 to 659 : 0.355 x (0.003 x i) = 0.001065 x i = 183.8403 million m
• sum i = 660 to 769 : 0.336 x (0.003 x i) = 0.001008 x i = 79.22376 million m
• sum i = 770 to 947 : 0.265 x (0.003 x i) = 0.000795 x i = 121.486335 million m

Add these together to get ~432.7 million meters of fingernails in the trash. Now we need to adjust the age groups for unique mortality rates. This will come in an edit.

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