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Solving Word Problems Involving Exponential Function

Updated on August 6, 2018

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

working

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