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Long story short, I'm writing a Hobbit fanfic and I'm trying to figure out how a Dwobbit would age. The equations I've been using for Dwarf and Hobbit aging are these:

Dwarf age equals half the human equivalent from 0-40, then D = H*4.2 - 44, where D = the adult Dwarven age, and H = the equivalent human age.

H = (h)*.6363, where H = the human age and h = the Hobbit age.

The problem is, I need an exponential graph for the Dwobbit age, since I would want them to age like Hobbits for the first, say, twenty years, then gradually slow to match Dwarven aging by the time they're 70. They would still come of age at the equivalent of 21, like a Hobbit, but at that point, their aging would match a Dwarf's and run parallel to it for the remainder of their lives.

So, theoretically, when Dw = 8, H = 5; Dw = 50, H = 16; Dw = 70, H = 21. The problem is, I can't figure out the equation. Any bored mathematicians want to help a writer out?

(P.S., if you want to help me consolidate the Dwarven equations into a single calculation, I'm not going to argue.)

Thank you in advance!

Edit: Got my numbers mixed up and then also realized that I was unclear.

NightAuthor
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  • How is $H=16$ when $Dw=50$? A dwarf would be $22$ and a hobbit would be $32$ by my reckoning based on what you wrote down. – spaceisdarkgreen Mar 06 '18 at 05:34
  • I'm sorry if it wasn't clear. H is the equivalent human age to any of the others, so an 8 year old Hobbit or Dwobbit would look the same as a 5 year old human, and a 70 year old Dwarf or Dwobbit would look the same as a 27 year old human or a 44 year old Hobbit. Then, a 50 year old Dwobbit would look the same as a 16 year old human, but a 50 year old Hobbit is middle-aged. But since Dwobbits wouldn't have a distinct shift from juvenile to adult aging like Dwarves, it would take them longer to catch up. Did that clarify anything? – NightAuthor Mar 07 '18 at 06:50
  • Dangit, I just realized the problem: Dwarves come of age at the human equivalent of 27, but Hobbits come of age at the equivalent of 21. The problem is, I want Dwobbits to come of age at the equivalent of 21, too, but to be aging as slowly as Dwarves at that point. I was unclear, that was my fault. Sorry! – NightAuthor Mar 07 '18 at 07:01
  • Yeah, but how long does it take a dwobbit to come of age? If I'm reading you right, Hobbits come of age at 33 (when their human-equivalent age is 21) and Dwarves come of age at 70 (when their human-equivalent age is 27). All of this is consistent with your formulas. The problem is that "coming of age" is a social construct. It has no direct bearing on their human-equivalent age. If you want them to age like hobbits for the first 30 or so years, and come of age at human-equivalent 21, then they come of age after about 33 years, like a Hobbit. – spaceisdarkgreen Mar 08 '18 at 01:51

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You have two points, so may as well just draw a line between them. You say that after $20$ years, the "age" of the Dwobbit should be the same as for a Hobbit, which rounds to $13.$ And after $70$ years, the age should be equivalent to that of a dwarf, which rounds to $27.$ The two points are then $(20,13)$ and $(70,27).$ So between $20$ and $70$ years, the aging rate is $$ \frac{27-13}{70-20} = 0.28,$$ so the equation is $$ H = 0.28\cdot Dw+b$$ where $b$ is the intercept. Plugging in $H=13$ and $Dw=20$ gives $$ b= 13-0.28\cdot 20 = 7.4$$ so we get $$ H = 0.28\cdot Dw +7.4$$ for when $20<Dw<70.$

spaceisdarkgreen
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