Echo date range in bash

gistfile1.txt

#!/usr/bin/env bash

# Snippet that finds the current date, subtracts a week, and
# echoes the date range from a week ago to current.

DATE=date
FORMAT="%Y-%m-%d"

now=`$DATE +$FORMAT`
start_time=`$DATE +$FORMAT -d "$now - 1 week"`

while [[ "$start_time" < "$now" ]] ; do
        start_time=`$DATE +$FORMAT -d "$start_time + 1 day"`
        echo "$start_time"
done