# 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**

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## Comments 6 comments

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

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

LORD

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

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

thank you because I have good assignment

6