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 ?
Formula to be used :
Pn=P(1 + r )^n
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 ?
Given : The rate of decay is i/2 or 0.5
P10=P( 1 -0.5 )^10
P10=20 ( .000976)
Problem Number Three :
A certain townhas a population of 50,000. Its rate increases 8% every six months. Find the population after four years ?
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
P= 20,000( 1 +.03)^12
P = 20,000 ( 1.426)
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 ( .000061035)
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