How do I preserve Exif Data when saving as a .TIF from Adobe Camera Raw?

[TheBiles]

I've noticed that my Exif Data looks vastly different when I save an image as a .JPG (example) compared to a .TIF (example). The shots straight from the camera as a .JPG also have much more detailed Exif Data (example). I mainly want to preserve the shutter speed, aperture, and ISO for reference purposes. So is there any way to retain the Exif Data when processing RAW, especially when saving to .TIF as opposed to .JPG?

Edit: Saving as a .TIF also seems to change the "taken" time/date to when ever I did the post-processing instead of when the shot was actually taken. Can this be fixed as well?

 

[AUG19]

I can save raw as TIF and retain that EXIF info (timestamp unchanged). Which software are you using?

 

[TheBiles]

I can save raw as TIF and retain that EXIF info (timestamp unchanged). Which software are you using?

The latest version of Adobe Camera RAW with Photoshop CS5 Extended.

 

[TheBiles]

Anyone?

Sent from my HTC Glacier

 

[AUG19]

You get my PM?

 

[TheBiles]

I did, but I'd like to know what's up with Photoshop in this situation or if I'm not doing something correctly on that end.

Sent from my HTC Glacier