8.7SolvingProblemswithExponentialandLogarithmicFunctions.notebookJanuary08,2015

Exponentialgrowth:

Exponentialdecay:

Halflife:

f(x)=P(1+r)x

f(x)=P(1r)x

f(x)=P(0.5)t/H

MindsOn:

Example1:Acertainvintagehockeycardincreasesinvalueby2.5%eachyear.Ifthecardisworth$854today,howmuchisitworthafter20years?

=854(1.025)20

=$1399.38

f(x)=P(1+r)n

ExponentialFunctions:

8.7SolvingProblemswithExponentialandLogarithmicFunctions.notebookJanuary08,2015

Example2:SwarmingdesertlocustsofAfricahavebeenknowntodamagepasturesandcropsaffectingmillionsofpeople.Aswarmof80millionlocustshavebeentreatedwithapesticidetocontroltheirpopulation.Thepopulationdecreasesby1/3eachday.Whatwillthelocustpopulationbein10days?

=80(2/3)10

=1.387million

f(x)=P(1r)n

Referencepoint

Intensity/valuebeingmeasured

Scaledmeasurement

Action:

8.7SolvingProblemswithExponentialandLogarithmicFunctions.notebookJanuary08,2015

pH scale:

Example3:AfishtankswaterwasrecentlychangedwithdistilledwaterofpH7.Thedayafteritwaschanged,applejuicewasspilledintoitwhichcausedthepHtodropto5.8.BywhatfactorhastheH+ionchanged?

TherelationshipbetweenpHandhydrogenionconcentrationisgivenbytheformula:

Where:[H+]istheconcentrationofhydrogenionsinmolesperlitre(mol/L)

pH=log[H+]

8.7SolvingProblemswithExponentialandLogarithmicFunctions.notebookJanuary08,2015

Example4:Howmanytimeslouderisarockconcertwithasoundintensityof123dBthanthethresholdofhearing?

Example5:InOctoberof2005,Pakistanexperiencedanearthquakeofmagnitude7.6resultinginthedeathofover73,000people.Lateronthatmonth,OwenSoundexperiencedanearthquakeof4.2inmagnitude.HowmanytimesmoreintensewasthePakistanearthquaketothequakeinOwenSound?

LetIPrepresenttheintensityofthePakistanquake

LetIosrepresenttheintensityoftheOwenSoundquake

and

WeneedtofindtheratioofIp/Ios:

and

=

ThePakistanearthquakewas2511.9timesmoreintensethantheOwenSoundquake.

Attachments

8.7SolvingProblemswithExponentialandLogarithmicFunctions.docx

8.7SolvingProblemswithExponentialandLogarithmicFunctions.pdf

8.7 Solving Problems with Exponential and Logarithmic Functions

Exponential Growth:

Exponential Decay:

Half-life:

Exponential Functions:

1. A certain vintage hockey card increases in value by 2.5% each year. If the card is worth $854 today, how much is it worth after 20 years?

2. Swarming desert locusts of Africa have been known to damage pastures and crops affecting millions of people. A swarm of 80 million locusts have been treated with a pesticide to control their population. The population decreases by 1/3 each day. What will the locust population be in 10 days?

Logarithmic Functions:

Scales that measure a wide range of values, such as the pH scale, Richter scale, and decibel scale, are logarithmic scales.

To compare concentrations on the pH scale, intensity on the Richter scale, or sound intensities, determine the quotient between the values being compared.

The relationship between pH and hydrogen ion concentration is given by the formula:

Where: [H+] is the concentration of hydrogen ions in moles per litre (mol/L)

3. A fish tanks water was recently changed with distilled water of pH 7. The day after it was changed, apple juice was spilled into it which caused the pH to drop to 5.8. By what factor has the H+ ion changed?

Decibel scale:

4. How many times louder is a rock concert with a sound intensity of 123 dB than the threshold of hearing?

5. In October of 2005, Pakistan experienced an earthquake of magnitude 7.6 resulting in the death of over 73,000 people. Later on that month, Owen Sound experienced an earthquake of 4.2 in magnitude. How many times more intense was the Pakistan earthquake to the quake in Owen Sound?

Pg. 499

#1 8, 10, 13 15, 18

SMART Notebook

8.7 Solving Problems with Exponential and Logarithmic Functions

Exponential Growth: Exponential Decay: Half-life:

Exponential Functions:

1. A certain vintage hockey card increases in value by 2.5% each year. If the card is worth $854 today, how much is it worth after 20 years? 2. Swarming desert locusts of Africa have been known to damage pastures and crops affecting millions of people. A swarm of 80 million locusts have been treated with a pesticide to control their population. The population decreases by 1/3 each day. What will the locust population be in 10 days?

Logarithmic Functions:

Scales that measure a wide range of values, such as the pH scale, Richter scale, and decibel scale, are logarithmic scales.

To compare concentrations on the pH scale, intensity on the Richter scale, or sound intensities, determine the quotient between the values being compared.

(

)

The relationship between pH and hydrogen ion concentration is given by the formula: Where: [H+] is the concentration of hydrogen ions in moles per litre (mol/L) 3. A fish tanks water was recently changed with distilled water of pH 7. The day after it was changed, apple juice was spilled into it which caused the pH to drop to 5.8. By what factor has the H+ ion changed?

8.7 Solving Problems with Exponential and Logarithmic Functions

Decibel scale:

4. How many times louder is a rock concert with a sound intensity of 123 dB than the threshold of hearing? 5. In October of 2005, Pakistan experienced an earthquake of magnitude 7.6 resulting in the death of over 73,000 people. Later on that month, Owen Sound experienced an earthquake of 4.2 in magnitude. How many times more intense was the Pakistan earthquake to the quake in Owen Sound? Pg. 499 #1 8, 10, 13 15, 18

SMART Notebook

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