The formula for calculating the percent change in a value between two points in time is:
#p = (N - O)/O * 100#
Where:
#p# is the percent change - what we are solving for in this problem.
#N# is the New Value - 7 pounds in this problem.
#O# is the Old Value - 12 pounds in this problem.
Substituting and solving for #p# gives:
#p = (7 - 12)/12 * 100#
#p = -5/12 * 100#
#p = -500/12#
#p = 41.7# rounded to the nearest tenth.
Phil's weight changed #color(red)(-41.7%)# during hibernation.
To gain his weight back Phil would go from #7# pounds (this is now the Old Value) to #12# pounds (this is now the New Value).
Substituting these values into the formula gives:
#p = (12 - 7)/7 * 100#
#p = 5/7 * 100#
#p = 500/7#
#p = 71.4# rounded to the nearest tenth.
Phil would need to add #color(red)(71.4%)# of his weight to get to the weight he was before hibernating.
