Warm Up 𝟐𝒓 𝒔 𝟑 ( 𝒓 𝟑 −𝟒𝒓 𝒔 𝟐 − 𝒓 𝟐 𝒔 𝟑 ) 4. 𝒙 𝒏−𝟏 𝒙 𝒏 Simplify each expression: 𝟐𝒓 𝒔 𝟑 ( 𝒓 𝟑 −𝟒𝒓 𝒔 𝟐 − 𝒓 𝟐 𝒔 𝟑 ) 4. 𝒙 𝒏−𝟏 𝒙 𝒏 𝟐𝟕 𝒂 𝟑 𝒃 𝟐 𝒄 𝟓 𝟒𝟓 𝒂 𝟒 𝒄 𝟐 𝟑 5. 𝒙 𝒏 + 𝒙 𝒏 3 𝑎 −2 3 ∙3 𝑎 5 6. 40 𝑥 −3 𝑦 4 5 𝑥 −5 𝑦 9

Test Results 2nd Period Average: 86.8% Median: 89.3% 3rd Period Average: 89.4% Median: 90.7% 4th Period Average: 85.6% Median: 88.0%

Exponents and Logarithms Chapter 5 Exponents and Logarithms

5.1 Growth & Decay: Integral Exponents 5.2 Growth & Decay: Rational Exponents Exponent Rules Growth and Decay Exponential Functions Solving Equations With Exponents

Laws of Exponents Same Bases Same Exponents If and only if x=y Ex: 5 2𝑥 = 5 16 means 2𝑥=16 𝑏≠0,−1,1

Laws of Exponents b0=1 or 𝑥 2 3 = 3 𝑥 2 𝑜𝑟 3 𝑥 2 4 3 2 = 4 3 = 64 =8

Exponential Equations 𝒇(𝒙)=𝒂 𝒃 𝒙 a = starting value b = multiplier x = time 𝑨 𝒕 = 𝑨 𝟎 (𝟏+𝒓) 𝒕 Exponential growth and decay- given a rate 𝑨 𝟎 = the initial amount, r = the rate as a decimal, t = time r is positive for growth, negative for decay t is positive for the future, negative for the past

5.1 Growth & Decay: Integral Exponents Currently, a hamburger costs $4.00. C(t) is an exponential function

5.1 Growth & Decay: Integral Exponents

r is positive for growth r is negative for decay

5.1 Growth & Decay: Integral Exponents

5.2 Growth & Decay: Rational Exponents

A population of 10000 frogs decreases at an annual rate of 22% A population of 10000 frogs decreases at an annual rate of 22%. How many frogs were there in 5 years ago? 1000 (0.78) −5 1000(1.22)5 1000 (1.22) −5 −1000(0.78)5

Given the equation 𝑦 = 2(0.63)𝒙, what is true? the starting point is smaller than the growth factor the equation is growing at 63% this is a linear equation the rate is -0.37

A type of bacteria has a very high exponential growth rate at 80% every hour. If there are 10 bacteria, determine how many there will be in 5 hours. 189 180 18.9 18

A species of extremely rare, deep water fish rarely have children A species of extremely rare, deep water fish rarely have children. If there are a 821 of this type of fish and their growth rate is 2% each month, how many will there be in half of a year? 821 52544 525.44 924

Given this table, what’s the equation? 𝑦 = 60(1.2) 𝒙 𝑦 = 50(2) 𝒙 𝑦 = 50(1.2) 𝒙 𝑦 = 60(2) 𝒙 𝒙 𝒚 50 1 60 2 72

A culture of bacteria contained 3,842,700 cells on one day and is growing at a daily rate of 6.8%. How many cells would be present 2 days and 9 hours later? 4,650,430 13,174,860 4,492,552 15,370,800

If there are 20 foxes in the forest this year, and 21 after one year, what is the growth rate of the foxes? a) 1% b) .5% c) .95% d) 5%

If the starting population of 5 rabbits grows at 200% each year, how many will there be in 20 years? 5(2)20 2(5)20 5(3)20 200(5)20

too many to fit on my calculator If the starting population of 5 rabbits grows at 200% each year, how many will there be in 50 years? 50000 3.6 𝑥 10 24 1600 too many to fit on my calculator

Class Exercises Pg 177 #1,2,5-9,13,17

Homework Page 173 #9,13,17,21,25,29,33,34,35 Page 178 #1,5,7,9,13,15,17,29,31,35,37

Simplify (3𝑦) 2 5

5.1 Growth & Decay: Integral Exponents

5.1 Growth & Decay: Integral Exponents

5.1 Growth & Decay: Integral Exponents Common Mistake Positive Exponents Common Denominator

5.1 Growth & Decay: Integral Exponents