# Solving Word Problems Involving Exponential Function

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

n=period

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)

P10=512,000

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

r=.08

n= (4)(2)= 8

P=50,000(1.08)^8

P=50,000(1.85)

P92,546

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

P=20,000

r= .03

m=1

t=12

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

SOURCE ;

ADVANCED ALGEBRA, TRIGONOMETRY AND STATISTICS BY

Orines

Esparrago

Reyes

## More by this Author

Lord De Cross 5 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!

LORD

cristina327 5 years ago from Manila Author

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 5 years ago

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

LORD

nerak 5 years ago

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

Student 3 years ago

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

grade 11 gen.math 4 months ago

thank you because I have good assignment