PH General Mathematics - Real-Life Application of Logarithmic Functions

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One of the major telecom conglomerates in the United States is Comcast. Their
connectivity media division Xfinity decides to launch an international tree-planting drive
in rural UAE as part of their “Green is Universal” program. Each employee of Xfinity
is required to donate a certain amount of money for every tree to be planted and all of
the proceeds will go to minimum-wage earners, distressed local workers, elderly in the
home-for-the-aged and their respective families.
Assuming that there are 90,000 of those people mentioned above inclusive of
their families, Comcast decides to aid them at a monthly rate of 20%. How many
months will it take for the company to help ¾ of its total number?
GIVEN:
a. 90,000 people to help
b. Comcast to aid at a 20% rate per month
c. Comcast to help ¾ of 90,000 people (67,500)
UNKNOWN:
the number of months it will take for Comcast to help 67,500 or ¾ of 90,000 people and
their families
FORMULA IN USE:
 =  (1 −  )
where...
A = ¾ of the number of people to help
P = total number of people to help
r = rate of help
t = time it will take for Comcast to help
SOLUTION:
 =  (1 −  )
log 0.75
67,500 = 90,000(1 − 0.20)
t = 1.289...
67,500
90,000
=
90,000(1−0.20)^
90,000
0.75 = 0.80
log 0.80 0.75 = 
Jose Lorenzo C. Barbasa
log 0.80
It will take Comcast 1.28
months or nearly a month and a
half to be able to help ¾ of the
total number of people and their
families.
11B – The Palm
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