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Solving Word Problems Involving Exponential Function

Updated on October 15, 2011

SolvingWord Problems Involving Exponential Function

Exponential function is one of the most important concept in Algebra. In this hub I present several problems involving exponential function with their solution. I hope you will find this hub useful and interesting.

Problem Number One :

Suppose a culture of 500 bacteria are put in a petri dish and the culture double very hour. How many bacteria will be left after ten hours ?

Solution :

Formula to be used :

Pn=P(1 + r )^n

WhereP=original population

r=rate of growth


Pn= Expected population after growth

Given :The rate of increase is100%or 1.

P10=P ( 1 + 1 )^10

P10=(500) (2 )^10

P10=500 ( 1024)


There will be512,000 bacteria after ten hours.

Problem Number Two :

A certain radioactive substance decays half of itself everyday. Initially there are 20 grams.How much substance will be left after ten days ?

Solution :

Given : The rate of decay is i/2 or 0.5

P10=P( 1 -0.5 )^10

P10=20 (0.5)^10

P10=20 ( .000976)

P10=0,01953 grams

Problem Number Three :

A certain townhas a population of 50,000. Its rate increases 8% every six months. Find the population after four years ?

Solution :

Given :

P= 50,000


n= (4)(2)= 8




There will be about 92,546 people after four years.

Problem Number Four :

Paolo deposits 20,000 pesos in a bank that pays 3% compound interest annually. How much money will he have after twelve year without withdrawal /

A=P ( 1+r/m )^mt

A= Total amount after t years

P= Principal amount

r= interest arte

m= number of time the amount is compounded a year


r= .03



P= 20,000( 1 +.03)^12

P = 20,000 ( 1.426)

P =28,515.28

Paolo’s money in the bank will be about 28, 515.218 after twelve years.

Problem Number Five :

The half-life of a radioactive substance is 12 hours and there are 100 grams initially. Determine the amount of substance remaining after one week.

The half-life of a radioactive substance is the amount of the time it takes for half of the substance to decay.

The exponential decay formula is :

A=Ao ( 1/2) ^t/k

Number of hoursin one week=(24)(7)=168 hours

A=100(1/2) ^168/12

A=(100) (1/2)^14

A=100 ( .000061035)

A=0.00610 grams







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    • profile image

      grade 11 gen.math 18 months ago

      thank you because I have good assignment

    • profile image

      Student 4 years ago

      thanks :D it helped but I hope had more problems to practice :D

    • profile image

      nerak 6 years ago

      this hub is very helpful for me...tnx a lot

    • Lord De Cross profile image

      Joseph De Cross 6 years ago

      yeah, Cristina we are around!...have a blessing day there too.


    • cristina327 profile image

      Maria Cristina Aquino Santander 6 years ago from Manila

      HI lord de cross it is great to hear from you again. Thank you for dropping by and appreciating this hub. YOur visit and comments are much appreciated. Blessings to you always and best regards.

    • Lord De Cross profile image

      Joseph De Cross 6 years ago

      As always very explained cristina. Just suggesting some pictures or color graphics... no that I intend to let you down. Good hub! voted up my friend!