pseudocode can be developed from rules of thumb.
    pseudocode: enter time in years, number of remaining root words
    pseudocode: output fraction of (remaining root words) over (root words at time zero)
    pseudocode: ouput remaining root words as fraction
    pseudocode: rules of thumb can be 3 to 15 percent off, partly since g..in g..out.
    pseudocode: need test cases > small,medium, giant
    pseudocode: need testcases within range of expected operation.
    pseudocode: are there any cases too small or large to be solved? 

        # pretty print from autoindent and ased editor  
        # human language root words calculator
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI , 2may2014
        package require Tk
        namespace path {::tcl::mathop ::tcl::mathfunc}
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} { time years :} }
        lappend names {   root words at time zero :}
        lappend names { root words remaining after t years: }
        lappend names { answers: ratio remaining over original at t :}
        lappend names { remaining roots percentage :}
        lappend names { remaining roots percentage :}
        lappend names { remaining roots percentage :}
        foreach i {1 2 3 4 5 6 7} {
    label .frame.label$i -text [lindex $names $i] -anchor e
    entry .frame.entry$i -width 35 -textvariable side$i
    grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 }
        proc pi {} {expr acos(-1)}
        proc about {} {
            set msg " Human Language Root Words
            from TCL WIKI,
            written on eTCL "
            tk_messageBox -title "About" -message $msg }
         proc calculate { } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 testcase_number 
            incr testcase_number           
            set years $side1  
            set roots1 $side2
            set roots2 $side3
            set percent 2.
   set percent [/ $roots1 [ expr { log(81) } ]    ]
            set modern_fraction [/ $percent 100. ]
            set side4 $modern_fraction
            set side5 $percent
            set side6 $percent
            set side7 $percent
            return $side5
             }
        proc fillup {aa bb cc dd ee ff gg} {
            .frame.entry1 insert 0 "$aa"
            .frame.entry2 insert 0 "$bb"
            .frame.entry3 insert 0 "$cc"
            .frame.entry4 insert 0 "$dd"
            .frame.entry5 insert 0 "$ee"
            .frame.entry6 insert 0 "$ff"
            .frame.entry7 insert 0 "$gg"}
        proc clearx {} {
            foreach i {1 2 3 4 5 6 7} {
                .frame.entry$i delete 0 end } }
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6 side7 testcase_number
            console show;
            puts "%| table |printed in| tcl wiki format|% "
            puts "&| quantity| value| comment, if any|& "
            puts "&| testcase number| $testcase_number||& "
            puts "&| time years at time zero :| $side1 ||&"
            puts "&| root words :| $side2 ||& "
            puts "&| root words  :| $side3 ||& "
            puts "&| answers: remaining root words ratio :| $side4 ||&"
            puts "&| remaining root words percentage:| $side5 ||& "
            puts "&| remaining root words percentage:| $side6 ||&"
           puts "&| remaining root words percentage:| $side7 ||&"
           }
         frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 1000. 200. 86.  .455   45.6  45.6   45.6  }
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 1000. 200. 86.  .455   45.6  45.6   45.6  }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 1000. 200. 86.  .455   45.6  45.6   45.6  }     
        ::ttk::button .clearallx -text clear -command {clearx 
        }
        ::ttk::button .about -text about -command about
        ::ttk::button .cons -text report -command { reportx }
        ::ttk::button .exit -text exit -command {exit}
        pack .calculator  -in .buttons -side top -padx 10 -pady 5
        pack  .clearallx .cons .about .exit .test4 .test3 .test2   -side bottom -in .buttons
        grid .frame .buttons -sticky ns -pady {0 10}
        . configure -background aquamarine4 -highlightcolor brown -relief raised -border 30
        wm title . "Human Language Root Words Calculator"      
 

  puts " %| testcase $testcase_number | value| units |comment |%"
  puts " &| volume| $volume| cubic meters |based on length $side1 and width $side2   |&"