" I think with most cancers you aren't fine on Monday and have a cancerous tumor by Friday" You have this wrong.. there are MANY more fast growing cancers then slow. Head and neck cancers, thyroid, pancreas, some of the lymphoma, leukemia, breast cancers, lung, bone and some of the brain cancers. For example Glioblastomas can literally double their size in a weeks time. And the way you stated this is completely wrong.
Once the cells are in you and replicating, you are no longer fine. And the tumor starts on Monday if you want to use your week as the example, it may just take until Friday to appear or be noticed so to speak.

Oh and your example of appendix cancer and carcinoid tumors are one in the same example.

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Be careful what you wish for.....