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.
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 $20<Dw<70.$