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**Exponential and Logarithmic Functions**

Solving Logarithm Properties Inverses Application Graphing 10 20 30 40 50

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**Solve, round to nearest hundredth**

5 2π₯+8 = 125 π₯ Answer

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5 2π₯+8 = 125 π₯ 5 2π₯+8 = 5 3π₯ 2π₯+8=3π₯ 8=π₯

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**Solve, round to nearest hundredth**

7( 5 π₯ )=168 Answer

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7( 5 π₯ )=168 5 π₯ =24 π₯= log 5 24 π₯= log 24 log 5 β1.97

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**Solve, round to nearest hundredth**

6 3π₯ β20=3 Answer

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6 3π₯ =23 3π₯= log 6 23 3π₯= log 23 log 6 3π₯β1.75 π₯β0.58

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**Solve, round to nearest hundredth**

3+ log 4 (π₯β7) =5 Answer

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3+ log 4 (π₯β7) =5 log 4 (π₯β7) =2 π₯β7= 4 2 π₯β7=16 π₯=23

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**Solve, round to nearest hundredth**

log (π₯+3) β log 4 =3 Answer

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log (π₯+3) β log 4 =3 log π₯+3 4 =3 π₯+3=4000 π₯=3997 π₯+3 4 = 10 3 π₯+3 4 =1000

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**Write in logarithm form**

π¦= 7 π₯ Answer

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log 7 π¦ =π₯

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**Write in exponential form**

π¦= log 3 π₯ Answer

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3 π¦ =π₯

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**Evaluate each of the expressions**

log 18 log 5 17 log 4 64 Answer

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log 18 β1.256 log 5 17 β1.760 log 4 64 =3

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**Simplify to a single logarithm**

2 log π β3 log π +4 log π Answer

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2 log π β3 log π +4 log π log π 2 β log π 3 + log π 4 log π 2 π log π 4 log π 2 π 4 π 3

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Expand the expression log 2 π 3 π 4 Answer

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log 2 π 3 π 4 log 2 π 3 β log π 4 log 2 + log π 3 β log π 4 log 2 +3 log π β4 log π

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Find the inverse. π¦=( 5) π₯+3 β4 Answer

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π¦=( 5) π₯+3 β4 π₯=( 5) π¦+3 β4 π₯+4=( 5) π¦+3 log 5 (π₯+4) =π¦+3 log 5 (π₯+4) β3=π¦

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Find the inverse. π¦=7 (2) π₯+5 Answer

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π¦=7 (2) π₯+5 π₯=7 (2) π¦+5 log 2 π₯ 7 β5=π¦ π₯ 7 = (2) π¦+5 log 2 π₯ 7 =π¦+5

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Find the inverse. π¦= log 8 π₯β7 Answer

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π¦= log 8 π₯β7 π₯= log 8 π¦β7 π₯+7= log 8 π¦ 8 π₯+7 =π¦

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Find the inverse. π¦=4 log (3π₯+7) Answer

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π¦=4 log (3π₯+7) π₯=4 log (3π¦+7) 10 π₯ 4 β7 3 =π¦ π₯ 4 = log (3π¦+7) 10 π₯ 4 =3π¦+7 10 π₯ 4 β7=3π¦

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Find the inverse. π¦= 1 3 ln (π₯+5) β2 Answer

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π¦= 1 3 ln (π₯+5) β2 π 3(π₯+2) =π¦+5 π₯= 1 3 ln (π¦+5) β2 π 3(π₯+2) β5=π¦ π₯+2= 1 3 ln (π¦+5) 3(π₯+2)= ln (π¦+5)

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**Suppose you deposit $1500 in a savings account that pays 6%**

Suppose you deposit $1500 in a savings account that pays 6%. No money is added or withdrawn form the account. Write an equation to model this situation. How much will the account be worth in 5 years? How many years until the account doubles? Answer

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**Suppose you deposit $1500 in a savings account that pays 6%**

Suppose you deposit $1500 in a savings account that pays 6%. No money is added or withdrawn form the account. Write an equation to model this situation. How much will the account be worth in 5 years? How many years until the account doubles? π¦=1500 (1+.06) π₯ π¦=1500 (1+.06) 5 = 3000=1500 (1+.06) π₯ 12 years π₯= log =11.896

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**In 2009, there were 1570 bears in a wildlife refuge**

In 2009, there were 1570 bears in a wildlife refuge. In 2010 approximately 1884 bears. If this trend continues and the bear population is increasing exponentially, how many bears will there be in 2018? Write an exponential function to model the situation, then solve. Answer

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**In 2009, there were 1570 bears in a wildlife refuge**

In 2009, there were 1570 bears in a wildlife refuge. In 2010 approximately 1884 bears. If this trend continues and the bear population is increasing exponentially, how many bears will there be in 2018? Write an exponential function to model the situation, then solve. π¦=π (π) π₯ π¦=1570 (1.2) π₯ π= =1.2 π¦=1570 (1.2) 9 8,100 bears

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**Suppose the population of a country is currently 7. 3 million people**

Suppose the population of a country is currently 7.3 million people. Studies show this countryβs population is declining at a rate of 2.3% each year. Write an equation to model this situation. How many years until the population goes below 4 million? Answer

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**Suppose the population of a country is currently 7. 3 million people**

Suppose the population of a country is currently 7.3 million people. Studies show this countryβs population is declining at a rate of 2.3% each year. Write an equation to model this situation. How many years until the population goes below 4 million? π=7.3 (1β0.023) π‘ 4=7.3 (1β0.023) π‘ π‘= log (0.5479) =25.854 26 years

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By measuring the amount of carbon-14 in an object, a paleontologist can determine its approximate age. The amount of carbon-14 in an object is given by y = aeο t, where a is the amount of carbon-14 originally in the object, and t is the age of the object in years. A fossil of a bone contains 32% of its original carbon-14. What is the approximate age of the bone? Answer

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π¦=π π β π‘ 32=100 π β π‘ 0.32= π β π‘ ln 0.32 =β π‘ ln β =π‘ π‘=9,496 years

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**A new truck that sells for $29,000 depreciates 12% each year**

A new truck that sells for $29,000 depreciates 12% each year. What is the value of the truck after 7 years? Answer

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π¦=29000 (1β0.12) π₯ π¦=29000 (1β0.12) 7 π¦=11,851.59 $11,851.59

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**Graph and Identify the domain and range**

π¦= 2 π₯β2 β3 Answer

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π¦= 2 π₯β2 β3 Domain: All real numbers Range: π¦>β3

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**Graph and Identify the domain and range**

π¦=2 2 π₯β3 +1 Answer

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π¦=2 2 π₯β3 +1 Domain: All real numbers Range: π¦>1

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**Graph and Identify the domain and range**

π¦= log 3 (π₯+1) +2 Answer

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π¦= log 3 (π₯+1) +2 Domain: π₯>β1 Range: All real numbers

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**Graph and Identify the domain and range**

π¦=2 log 5 (π₯) β3 Answer

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π¦=2 log 5 (π₯) β3 Domain: π₯>0 Range: All real numbers

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**Graph and Identify the domain and range**

π¦=β3 2 π₯+1 +2 Answer

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π¦=β3 2 π₯+1 +2 Domain: All real numbers Range: π¦<2

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Objectives Use the number e to write and graph exponential functions representing real-world situations. Solve equations and problems involving e or natural.

Objectives Use the number e to write and graph exponential functions representing real-world situations. Solve equations and problems involving e or natural.

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