# PH General Mathematics - Real-Life Application of Logarithmic Functions

```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 &frac34; 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 &frac34; of 90,000 people (67,500)
UNKNOWN:
the number of months it will take for Comcast to help 67,500 or &frac34; of 90,000 people and
their families
FORMULA IN USE:
𝐴 = 𝑃 (1 − 𝑟 )𝑡
where...
A = &frac34; 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:
𝐴 = 𝑃 (1 − 𝑟 )𝑡
log 0.75
67,500 = 90,000(1 − 0.20)𝑡
t = 1.289...
67,500
90,000
=
90,000(1−0.20)^𝑡
90,000
0.75 = 0.80𝑡
log 0.80 0.75 = 𝑡
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 &frac34; of the
total number of people and their
families.
11B – The Palm
```