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PERFORMANCE TASK IN GENERAL MATHEMATICS
Name: Mark Froilan C. Vallejos Section: 11- Gas A
Directions: Read each item carefully and solve for what is asked. Show your solution and make sure to answer
all the questions.
RATIONAL FUNCTION
Bill can finish a report in 2 hours. Maria can finish the same report in 4 hours. How long will it take them to
finish the report if they work together? If they will start to work at 6pm, what time would they finish?
Answer: Work Rate Solution
Report: 1
x
Bill:
x
Maria:
x
( cross multiply )
Working Together: 1/x 3 x = 4
3 x
∨1.33 hours
*Working together, Bill and Maria can finish the same report in 4/3 hours or 1.33 hours.
*If they will start to work at 6pm, they would finish the report at 7pm.
INVERSE FUNCTION
You and a friend are playing a number-guessing game. You ask your friend to think of a positive number,
square the number, multiply the result by 2, and then add 3. If your friend’s final answer is 53, what was the
original number chosen? Use the concept of inverse function in your solution.
Answer: Solution
2 x
2
2 x
2
*The original number that was chosen is 5.
2 x
2
x
2
x = 5
EXPONENTIAL FUNCTION
Supposed you need Php 30,000 in the next 10 years for a holiday trip, and you invested Php 1,000 in an
account paying an annual percentage rate of 12% compounded annually, how much would you have in your
account at the end of 10 years?Would it be enough for your planned trip?
Answer: Solution
f ( x )= a ( 1 + r )
x
*In 10 years, my account would have ₱3 110.
f ( x )= 1000 ( 1 +0.12)
10
*It would not be enough to my planned trip since the trip
f ( x )= 1000 ( 1.12)
10
needs ₱30 000. Base on my own calculations, in order to
f ( x )= 1000 (3.11) have a ₱30 000 in the next 10 years with the rate of 12%
f ( x )=3,110 the starting investment must be ₱9 646.
LOGARITHMIC FUNCTION
Suppose that Vina invests Php 10,000 in an investment earning 5% per year for her to start a business in the
next 5 years. How long it would take his investment to be Php 50,000? Will she able to reach hit the timeline
of her goal?
Answer: Solution
f
x
= a ( 1 + r )
t
t
*It would take 33 years in order that
t
his investment to grow ₱50 000.
t
*Nope, she will unable to reach hit the timeline
log 5 = t log 1.05 of her goal.
log 5
log 1.
= t
log 1.
log 1.
log 5
log 1.
= t
32.99 years = t
¿ 33 years
