Otherapplicationsare introducedin the exercises.
ReviewQuestions
- In 1990,the populationof the USAwas million.Assumethat the annualgrowthrate is (a)
Accordingto this model,whatwas the populationin the year 2000?(b) Accordingto this model,in which
year the populationwill reach billion? - Provethat if a quantity is exponentiallygrowingand if is the valueat and at time then
the growthrate will be givenby - Newton’s Law of Coolingstatesthat the rate of coolingis proportionalto the differencein temperature
betweenthe objectand the surroundings.The law is expressedby the formula
where is the initialtemperatureof the objectat is the roomtemperature(the surroundings),
and is a constantthat is uniquefor the measuringinstrument(the thermometer)calledthetime constant.
Supposea liter of juice at is placedin the refrigeratorto cool.If the temperatureof the refrigeratoris
kept at and whatis the temperatureof the juice after minutes?
- Referringback to problem3, if it takesan object secondsto cool from aboveroomtemperature
to aboveroomtemperature,how long will it take to cool another? - Polonium-210is a radioactiveisotopewith half-lifeof days.If a samplehas a massof grams,
how muchwill remainafter weeks? - In the physicsof acoustics,thereis a relationshipbetweenthe subjectivesensationof loudnessand the
physicallymeasuredintensityof sound.This relationshipis calledthesoundlevel It is specifiedon a
logarithmicscaleand measuredwith unitsofdecibels. The soundlevel of any soundis defined
in termsof its intensity (in the SI-mksunit system,it is measuredin wattsper metersquared, )
as
For example,the averagedecibellevelof a busystreettraffic is normalconversationat a dinner
tableis , the soundof leavesrustlingis , the sirenof a fire truckat metersis
and a loud rock concertis The soundlevel is consideredthe thresholdof pain for the
humanear and is the thresholdof hearing(the minimumsoundthat can be heardby humans.)
a. If at a heavymetalrock concerta meterregistered whatis the intensity of this sound
level?