How to properly access a variable outside a function in shell?

#! /bin/bash


number=$1

if [ "$1"  -le 1 ] ;

then
        echo -e "Number can not be negative or equal to 1, pleaes enter a new number.\n";
        exit
fi;

recur_fib()
{
  first_num=$1

  #start time
  START=$(date +%s%6N);

  [ $first_num -lt 2 ]  && echo -n $first_num || echo -n $(( $( recur_fib $(( first_num - 1 )) ) + $( recur_fib $(( first_num - 2 )) ) ))

  #end time
  END=$(date +%s%6N)

 let  elapsed=$END-$START | bc

}

totaltime=$(recur_fib $elapsed)
#recursive
val_recur=$(recur_fib $1)

#nonrecursive

nonrecur_fib()
{
  first_num=$1
  first_fib=0
  second_fib=1

  #start time
  start_time=$(date +%s%N)

  #loop for nonrecur
  for ((number=0; number<=first_num; number++))
    do
        echo -n "$first_fib "
        total=$((first_fib+second_fib))
        first_fib=$second_fib
        second_fib=$total
    done
  #end time
  end_time=$(date +%s.%6N)
  let nonrecur_time=$end_time - $start_time 
}

#without recursion
val_without=$(nonrecur_fib $1)

total_nonrecur_time=$(nonrecur_fib $nonrecur_time)

  #date and time
  echo START: `date +"%m-%d-%Y %H:%M.%S.%N"` | tee -a fibonacci.out

  #allowing user to enter R or r and N or n to chose the method
  echo "Please enter the method you would like to use to calculate the sequence Non-recursive(N) or Recursive(R)"
  read method

  #telling the user the calculations will start
  echo -e "The calculations will start now"

case $method in
#case for nonrecursive
        "N" | "n")
                echo -e "NON-RECURSIVE $1\n" | tee -a fibonacci.out

                echo -e "Run\tFibonacci\t\t\tTime" | tee -a fibonacci.out

                 count=1
                while [ $count -le $1 ]
                do
                        echo -e "$count" '\t' $val_without '\t''\t''\t' $total_nonrecur_time | tee -a fibonacci.out
                        ((count = count + 1))

                done

                echo Average Time: $(((count * total_time1) / count))
                echo END: `date +"%m-%d-%Y %H:%M.%S.%N"` | tee -a fibonacci.out
                echo Total time: $((count * total_nonrecur_time)) | tee -a fibonacci.out
                echo "Run is done" | tee -a fibonacci.out

                ;;
#case for recursive
        "R" | "r")
                #repeat the the method and number chosen
                echo -e "RECURSIVE $1\n" | tee -a fibonacci.out

                echo -e "Run\tFibonacci\tTime" | tee -a fibonacci.out

                count=1
                while [ $count -le $1 ]
                do
                        echo -e "$count" '\t' $val_recur '\t''\t' $totaltime | tee -a fibonacci.out
                        ((count = count + 1))

                done

                #shows average time
                echo Average Time: $(((count * totaltime) / count)) | tee -a fibonacci.out
                #shows end time
                echo END: `date +"%m-%d-%Y %H:%M.%S.%N"` | tee -a fibonacci.out
                #shoes total time
                echo Total time: $((count * totaltime)) | tee -a fibonacci.out
                echo "Run is done" | tee -a fibonacci.out
                ;;
        *)
                echo "Please chose either R,r or N,n"