advertisement

Pre-Calculus Unit 10 Exam: Name ___________________________ βExponential and Logarithmic Functionsβ (Practice Exam) (10-1) Sketch each exponential function by hand. #1 π¦ = 2π₯ #2 π(π₯ ) = 4βπ₯ #3 The function below π¦1 = π π₯ . Give an expression for π¦2 below. #4. An investment of $11,000 earns interest (10-2) compounded continuously at a rate of 8%. What will its value be after 20 years? #5. A known radioactive isotope has a half-life of 1288 years. A certain sample of the isotope can be modeled by 1 π‘/1288 π¦ = 60 ( ) , where y is the amount of 2 the isotope present (in grams) after t years. (a) What is the initial mass of the sample? (b) How much of the sample will be left after 3000 years? #6. Evaluate each expression. (10-3) (a) log 3 243 1 (b) log 5 25 (c) ln(π 8 ) (d) log 6 1 (10-4) Sketch each function by hand. #7. π(π₯ ) = log 2 π₯ #8. π(π₯ ) = β log 4 π₯ (10-5) Evaluate. #9 log 4 10 #10. log 2.7 1.82 Expand each expression. #11. ln(ππ₯ 2 ) #12. log π (π§ ) 1 Condense each expression. #13. #14. 1 2 ln π + ln π β 3 ln π 2(log π π + log π π) β log π (π₯ β 5) (10-6) Solve each equation. 1 #15. 5π₯ = #16. π 3π₯ = 11 #17. 6 β 2π₯ + 4 = 37 625 (10-7) Solve each equation. #18. log 10 π₯ = 3.6 #19. β ln(ππ₯ ) + 3 = β9 #20. log π π₯ + log π (π₯ β 4) = log π 5 #21. Given the population data below for bacteria (10-8) in a petri dish: Time (hrs.) 0 2 3 5 6 8 11 Population 30 61 88 151 179 355 768 (a) Find a best-fitting exponential model of the form π¦ = π β ππ₯ , where y is the population in the dish after x hours. (b) Use the model from (a) to predict the population of the dish after 24 hours. #22. Given the data below: (10-9) x 0.5 1 2 5 8 10 17 y -3 1 1.4 3 3.9 4.4 5.3 (a) Find a best-fitting logarithmic model of the form π¦ = π + π β ln π₯ for the data. (b) Use the model from (a) to predict the value of x when y = 8.