# nSolve gives answer on CAS but not numeric nspire

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### Peggy Frisbie

Oct 24, 2022, 5:57:16 PM10/24/22
to tinspire
My students had a problem about a half-life of 2.46 × 10⁵, and the equation to be solved was 0.7 = (1/2)^(t/246000). Using nSolve (not the CAS solve command), the CAS calculators will solve it correctly, but the numerical calculators give "No solution found" as a result. The answer, to the nearest whole year, is 126585.

I discovered after looking through posts here that if I give a starting value (lower bound) of 100000 or 125000, I get the solution on the numeric calculator, but not for a starting value of 10000. Also, if I use the "x =" version of the guess, 126000 doesn't find the answer but 127000 does.

Does anyone know what the calculator is doing here? I've pointed this out to the kids as why we also need to be able to solve graphically, but that's kind of unsatisfying. I don't get why the two calculators would do different things with the same numerical solve command.

Screen shots to show the CAS and numerical results for the same command: