Chapter 12 Logarithmic Exponential Functions Section 5 Applications

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Concept Compound Interest 1 If P dollars are deposited in an account that pays

Example Compound Interest If $6000 is invested in an account that pays 6% annual

Concept 3 Continuous Compound Interest If P dollars are deposited in an account that

Example Continuous Compound Interest If $10, 000 is invested in an account that pays

Concept Exponential Growth 5 If a quantity increases at an exponential rate, then its

Example Exponential Growth (page 1) 6 In 1993, Visalia’s population was 80, 000. In

Example Exponential Growth (page 2) 6 It will take approximately 34 years, or until

Concept 7 Exponential Decay If a quantity decreases at an exponential rate, then its

Example 8 Exponential Decay The half-life of a particular radioactive substance is 8 days.

Concept 9 p. H The p. H of a liquid is calculated using the

Example 10 p. H If the concentration of hydrogen ions for a certain liquid

Concept 11 Volume of a Sound The volume (L) of a sound in decibels

Example Volume of a Sound (page 1) 12 Find the intensity of a sound

Example Volume of a Sound (page 2) 12 The intensity is watts per square

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Concept Compound Interest 1 If P dollars are deposited in an account that pays an annual interest rate r that is compounded n times per year, then the amount A in the account after t years is given by the formula Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 3

Example Compound Interest If $6000 is invested in an account that pays 6% annual interest, compounded quarterly, what will the balance be in 10 years? 2 The balance will be $10, 884. 11. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 4

Concept 3 Continuous Compound Interest If P dollars are deposited in an account that pays an annual interest rate r that is compounded continuously, then the amount A in the account after t years is given by the formula Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 5

Example Continuous Compound Interest If $10, 000 is invested in an account that pays 7% annual interest, compounded continuously, how long will it take for the investment to double? 4 It will take approximately 9. 9 years. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 6

Concept Exponential Growth 5 If a quantity increases at an exponential rate, then its size P at time t is given by the formula represents the initial size of the quantity, while k is the exponential growth rate. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 7

Example Exponential Growth (page 1) 6 In 1993, Visalia’s population was 80, 000. In 2008 the population reached 120, 000. When will the population reach 200, 000? Find k. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 8

Concept 7 Exponential Decay If a quantity decreases at an exponential rate, then its size P at time t is given by the formula represents the initial size of the quantity, while k is the exponential decay rate. Half-Life The half-life of a radioactive element is the amount of time that it takes for half of the substance to decay. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 10

Example 8 Exponential Decay The half-life of a particular radioactive substance is 8 days. If 20 grams of the substance is initially present, how many grams will remain in 30 days? There will be approximately 1. 5 grams. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 11

Concept 11 Volume of a Sound The volume (L) of a sound in decibels is given by the formula where I is the intensity of the sound in watts per square meter. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 14