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AFM EXPONENTS AND LOGS TEST REVIEW Name ________________________________ Date ______________ Per ______________ Show your work on a separate sheet of paper. Circle or box your answers. VOCABULARY Domain Common Log Range Natural Log Asymptote Exponential Function FUNCTIONS 1. Is 𝑦 = 5(1.2)𝑥 exponential growth or decay? Justify your response. NATURAL LOGS & e Sketch the graph on graph paper. State the domain, range, intercepts, asymptotes, end behavior, and transformation. 15. 4e 2 x 15 7 2. 𝑓(𝑥) = 3(2)𝑥−1 + 4 3. 𝑓(𝑥) = log 3 (𝑥 + 1) − 2 Logarithm Principal 14. ln x 4 5 16. ln x ln 4x 10 17. 𝑒 𝑥 ∙ 𝑒 4𝑥 = 7 EXPONENTIAL EQUATIONS EXPONENTIAL GROWTH & DECAY 4. Solve: 252 x 125 x 2 18. A radioactive substance has a half-life of 26 years. Find the rate of decay. 5. Solve: 2187 x 9 813 x 7 LOGS 6. Write 46 4096 in log form. 7. Write log 9 27 3 in exponential form. 2 Solve for x. 8. log 2 x 6 5 9. 20. In a laboratory, an organism grows from 100 to 250 in 8 hours. What is the hourly growth rate? 21. John invests $3,000 in a savings account that has a 3.25% annual interest rate. What will the account balance be if he leaves the money in the account for 12 years, without making any withdrawals or deposits? 34 x 33 x 10. log 5 4 x 1 log 5 3x 2 19. A current census shows that the population of a city is 3.5 million, and the population is growing at a constant rate of 1.1%. Find the population of the city in 30 years. 2 11. log 2 9 x 5 2 log 2 x 1 22. A computer system depreciates at an average rate of 4% per month. If the value of the computer system was originally $12,000, in how many months is it worth $7350? x 3 12. 2 5 13. log 6 48 log 6 16 log 6 5 log 6 5 x 5 23. A music store sold 200 guitars in 2007. The store sold 180 guitars in 2008. The number of guitars that the store sells is decreasing exponentially. If this trend continues, how many guitars will the store sell in 2012?