The following warnings occurred:
Warning [2] Undefined array key 23686 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $thread - Line: 295 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 295 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Trying to access array offset on value of type null - Line: 295 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 295 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $fid - Line: 295 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 295 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 23686 - Line: 331 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 331 errorHandler->error_callback
/inc/plugins/threaded_mode.php 304 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $theme - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Trying to access array offset on value of type null - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $theme - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Trying to access array offset on value of type null - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $lang - Line: 5 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 5 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Attempt to read property "messages_in_thread" on null - Line: 5 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 5 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks





More = Less (x2^(Time/Halftime)



#2

No, this isn't a sermon on the spiritual hazzards of collecting too many HP calculators! The relation dN/dt=kN occurs all over the place in the physical and biological sciences -- in first order chemical reactions, radioisotope decay, simple biological turnover, microbial population growth, the absorption of electromagnetic radiation by matter, the discharge of a capacitor, etc. etc. I used to teach a course on the applications of radioisotopes to biology (back in the sixties), and my students and I would spend hours with slide rules and semi-logarithmic paper, calculating and plotting the decay or build-up of materials. There are four variables in the integrated solution, N2 = N1*e^kt, so one has four different possible cases to solve for. Since there are so many different applications of this "compound interest" relationship, one can wind up with a library of equations as one roves around the various sciences.

But with the solve routine of the 19B or 27S or 17B etc. calculators, one can cover all the possibilities with the one statement: MORE = LESS x 2^(TIME/HFTM), or if one prefers the natural base, with MORE = LESS x EXP^(TIME/TRTM), where HFTM stands for half-time, and TRTM stands for turnover time (=1.44xhalftime). It doesn't matter which way time is flowing in the actual case, whether towards decrease or increase -- you know which it is, and the calculator doesn't care. With the numerical solve routine, you give the calculator three of the factors and it solves for the fourth, whichever it is. And of course "time" and "half-time" can actually stand for "distance" and "half-distance" if that is the nature of the physical problem.

I find it almost indecent that so much can be done with so little -- but that is also the joy, to one brought up in the age of trig and log tables, of the little pocket calculator.


Possibly Related Threads…
Thread Author Replies Views Last Post
  [HP Prime]How to get Discrete-Time Fourier Transform uklo 0 1,484 11-18-2013, 08:02 PM
Last Post: uklo
  Date/time formats R. Pienne 4 2,164 11-01-2013, 12:43 PM
Last Post: Marcus von Cube, Germany
  How to set the Date.Time etc on a WP34S Harold A Climer 4 1,862 10-29-2013, 09:32 PM
Last Post: FORTIN Pascal
  Prime: Exam mode (possible duplicate after funny response first time) Paul Townsend (UK) 1 1,442 10-24-2013, 03:09 PM
Last Post: Tim Wessman
  Date/time programs for the HP 35s R. Pienne 0 1,067 10-03-2013, 02:37 PM
Last Post: R. Pienne
  Nothing like passing the time away... Eddie W. Shore 2 1,361 03-21-2013, 08:23 AM
Last Post: Eddie W. Shore
  New compile-time options for WP-34S Nigel J Dowrick 15 4,591 01-29-2013, 03:25 PM
Last Post: Stephan
  Date & Time disappear on WP 34S RenĂ© Franquinet 16 5,119 12-10-2012, 08:24 AM
Last Post: Walter B
  In time for HHC 2012 ... Walter B 4 1,648 09-09-2012, 05:30 AM
Last Post: fhub
  Any informal HHC2012 time set aside for WP34S??? Namir 8 2,404 09-07-2012, 09:26 AM
Last Post: Eddie W. Shore

Forum Jump: