If you throw some data at a clustering algorithm, the clustering algorithm is guaranteed to give you clusters back. So I'm not convinced about the results suggesting a precise pattern of rapid aging.
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Anecdotally I feel I noticed a very fast ageing speed between 38 and 40. Suddenly got white hairs, feel more tired, more wrinkles, way harder to keep VO2max up (I run a lot), muscle sores after training suddenly lasting up to 3 days instead of 1, face looks older, etc.
I feel like that all happened real fast around this age.
It's like there's two versions of me now, the one who was somehow moderately fit by biochemical decree, with a healthy amount of flesh to his face, voluminous dark blonde hair and a pleasant complexion...
... And the grey haired, weathered, lined, dessicated mummy I see in the mirror. I love my kids dearly but the constant caring really takes something out of you. That and the whole getting older thing in TFA.
I keep telling myself I'll get a gym membership soon to reclaim some of my dignity.
Looking back at pictures from really not that long ago (less than 5 years) to before kids or the first year of the first kid and one of the overriding comments both me and wife have are "We look so young!". We have two aged 3-to-5, and its been hard but not that hard, especially now that there are no nappies/diapers and they sleep 10-11 hours straight overnight and we pay for gardeners, cleaners etc and pretty much do our usual 9-5 as we did before kids.
FWIW though, I would say that you don't need a gym membership. I try to run/jog/saunter a couple of times a week - its free and easy to do. Getting started is as easy as putting some shoes on and stepping out your door - no set up, no memberships, no travel to get to the place to do the running etc. You don't need to go buy special shoes or anything - just something vaguely appropriate will be fine to get started with for short distances and steady pace.
Its what your body has evolved to do, and I think there is a good mental-health aspect to just going out on your own and running and letting the mind wander. I personally don't especially "enjoy" running, and it is sometimes hard to persuade myself to actually go do it, but once I have started and I am 5-10 minutes in, it's quite nice.
Good luck