1. 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 ) 𝒙 𝒏−𝟏 𝒙 𝒏
𝟐𝟕 𝒂 𝟑 𝒃 𝟐 𝒄 𝟓 𝟒𝟓 𝒂 𝟒 𝒄 𝟐 𝟑 𝒙 𝒏 + 𝒙 𝒏
3 𝑎 −2 3 ∙3 𝑎 𝑥 −3 𝑦 4 5 𝑥 −5 𝑦 9

2. 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%

3. Exponents and Logarithms
Chapter 5
Exponents and Logarithms

4. 5.1 Growth & Decay: Integral Exponents
5.2 Growth & Decay: Rational Exponents
Exponent Rules
Growth and Decay Exponential Functions
Solving Equations With Exponents

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

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

7. 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

8. 5.1 Growth & Decay: Integral Exponents
Currently, a hamburger costs $4.00.
C(t) is an exponential function

9. 5.1 Growth & Decay: Integral Exponents

10. r is positive for growth
r is negative for decay

11. 5.1 Growth & Decay: Integral Exponents

12. 5.2 Growth & Decay: Rational Exponents

14. A population of 10000 frogs decreases at an annual rate of 22%
A population of 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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%

21. 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

22. 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
1600
too many to fit on my calculator

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

31. 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

32. Simplify (3𝑦) 2 5

33. 5.1 Growth & Decay: Integral Exponents

34. 5.1 Growth & Decay: Integral Exponents

35. 5.1 Growth & Decay: Integral Exponents
Common Mistake
Positive Exponents
Common Denominator

36. 5.1 Growth & Decay: Integral Exponents