Let me present an axiom of software engineering: "The effort (cost) to fix a software defect is proportional to the time between defect's introduction and discovery".
Please note, that the axiom does not say "100x more", it says that cost increases (usually; it may even decrease, why not? consider a bug in ransomware that prevents it from encrypting files properly). The concrete cost may be 1.5x, 10x or 1Mx, it all depends on the circumstances.
It might be a rule of thumb, but it's not an axiom (otherwise, there could be no counterexamples). Some software defects are only discovered years later, but can be fixed in minutes.
Please note, that the axiom does not say "100x more", it says that cost increases (usually; it may even decrease, why not? consider a bug in ransomware that prevents it from encrypting files properly). The concrete cost may be 1.5x, 10x or 1Mx, it all depends on the circumstances.
And here's a pretty picture from the research paper on the subject: https://www.researchgate.net/figure/Cost-of-Fixing-a-Defect-...