Honors Algebra I Exponential Review PDF

Honors Algebra I Exponential Review Name________________________________ 1. Simplify the expression. 5 3 6 a) 4 · 4...

Honors Algebra I Exponential Review Name________________________________ 1. Simplify the expression. 5 3 6 a) 4 · 4 b) 3 ( 5) c) (− 2 · 5) 5 4 7 2 −3 3 4 2 d) 3𝑥 · 5𝑥 [ e) (𝑥 + 3) ] ( f) − 2𝑥 ) (3𝑥2) 2 2 8 6 7 g) − ( 𝑥)1 2 h) 7 7 3 i) 𝑥𝑦 4𝑥 4 3 3 5 2 2 l) ( 2 −5) 2 −2 5 3 j) − 3 ·3 ( k) − 3 · 2 ) 2𝑥 𝑦 4𝑥 𝑦 −2 3 −2 3 ( ) ( )( ) ( ) 3 −2 −3 2 −5 2𝑥 2𝑥 4𝑥 6𝑥 𝑦 𝑧 m) − 6 n) 2 4 o) 5 −3 2 3𝑦 𝑦 3𝑦 2𝑥 𝑦 𝑧 2. Find the missing exponent. −4 ? −2 ( ) 4 ? ? 4 5 7 6 12 a) 2𝑥 𝑦 · 3𝑥 𝑦 = 6𝑥 𝑦 b) 5𝑥( ) = 𝑥 25 c) 𝑥 2 = 16𝑥 𝑥 2 𝑥 = 𝑏 and ( 3𝑦) = 𝑏 𝑏 9 𝑏 13 3. Find the value of x and y if 𝑦 𝑏 𝑏 4. Find the value of the following. 2 2 4 1 −3 4 −2 a) 8 3 b) − 32 5 c) 27 d) ( ) 9 5. Determine if the following represents a linear function, an exponential function or neither. Then find the equation if it’s a linear or an exponential. x 0 1 2 3 4 y 1 2 6 24 120 6. Determine if the following represents a linear function, an exponential function or neither. Then find the equation if it’s a linear or an exponential. x 0 1 2 3 4 5 y 5/2 5 10 20 40 80 7. Determine if the following represents a linear function, an exponential function or neither. Then find the equation if it’s a linear or an exponential. x 1 2 3 4 5 6 y 6 18 54 162 486 1458 8. Determine if the following represents a linear function, an exponential function or neither. Then find the equation if it’s a linear or an exponential. x 0 1 2 3 4 5 y 1/2 1/6 1/18 1/54 1/162 1/486 9. Determine if the following are exponential growths or decays. 7 𝑥 2 −𝑥 a) 𝑦 = 2(4) 𝑥 b) 𝑦 = 3 2 ( ) 4 c) 𝑦 = 9 ( ) 9 10. Write a function for the following graphs. 11. Graph the following. 𝑥 a) 𝑦 = 2(2) 𝑥 b) 𝑦 =− 3 12. Suzy bought a piece of office equipment in 2015 for $875. It depreciates at 13% per year. Write a function to represent the value of the equipment in any given year. What is the expected value in 2023? 13. The population of the town Suzyville has been growing by 7% each year since 1997. In 1997, there were 50,320 people in Suzyville. Write a function to represent the population in any year. What is the expected population of Suzyville in 2025? 14. Suzy received a car worth $20,000 on her 16th birthday. It depreciates at 9% per year. Write a function to represent the value of the car after any number of years. What was the car worth on Suzy’s 21st birthday? 15. Suzy was doing an experiment on the growth of bacteria. She started out with 350 and they were growing 3.5% per hour. Write a function to represent the number of bacteria at any given time. How many bacteria will there be in 2 days? 4 16. Write a word problem that would give the following function, 𝑦 = 312(. 86). 17. Determine if the following sequences are arithmetic, geometric or neither. If they are arithmetic or geometric find a rule (equation) for 𝑎𝑛. a) 12, 5, − 2, − 9,... b) 1, 2, 4, 9, 16... c) 2, 8, 32, 128,... 1 1 7 13 2 2 d) 8, 4, 2, 1, 2 ,... e) 2 , 2, 2 , 5, 2 ,... f) 6, 2, 3 , 9 ,... 18. The first 3 terms of a sequence are given, find the 𝑎13 (the 13th term). − 8, − 1, 6 19. The first 3 terms of a sequence are given, find the 𝑎21 (the 21st term). 3, 6, 12 20. The first 3 terms of a sequence are given, find the 𝑎42 (the 42nd term). 5, 15, 20