Integrated Math 3 Name 2023 Kuta Software LLC. All rights reserved #21 Graphing Logs, Domain & Range Date Period Identify the domain and range of each. Then sketch the graph. 1) y = log (x +2) 2) y = log 2 (x - 1) - 3 3) y = log (x + 5) 4) y = log, (x - 3) +5 -8 5) y = log, (x+ 5) -4 6) y = log (x - 1) - 11B. A veterinarian has instructed Harrison to give his 75-lb dog one 325-mg aspirin tablet for arthritis. The amount of aspirin A remaining in the dog's body after t minutes can be expressed by A = 325%)? How long will it take for the amount of aspirin to drop to 50 mg? Exponential and Logarithmic Functions #19 mm " ' " EXERCISE COMPOUND INTEREST In Exercises 1522, complete the table for a savings account in which interest is compounded continuously. Initial Annual Time to Amount After Investment % Rate Double 10 Years 15. $ 1000 3.5% ). $750 10% -"-"'_"\""- 17. $750 7% yr K $10,000 ..,_ 12 yr _.-- 19. $500 $1505.00 16'. $000 , *- $19,205.00 21. 4.5% $10,000.00 '}{' 2 e , __.,-- $2010.00 43. POPULATION The populations P (in thousands) of Horryr County. South Carolina from 1970 through 20071 can be modeled by P = 13.5 + 92.2.2002\"?! where t represents the year, witht = 0 corresponding to 1970. (Source: US. Census Bureau} (0) Use the model to complete the table. Year 1970 1980 1990 2000 2007 Population (h) According to the mode], when will the population of Horry County reach 300.000? (0) Do you think the model is valid for long-term predictions of the population? Explain. n a u 1. A person invests $2560 in an account that earns 5.2% annual interest. Find when the value of the investment reaches $6000. 2. A person invests $1800 in an account that earns 2.46% annual interest. Find when the value of the investment reaches $3500. 3. A person invests $6750 in an account that earns 6.23% annual interest compounded continuously. Find when the value of the investment reaches $15,000. 4. A person invests $465 in an account that earns 3.1% annual interest compounded continuously. Find when the value of the investment reaches $2400. Solve. 5. The price P of a gallon of gas after t years is given by the CIT equation P = Po(1 + r)', where Po is the initial price of gas and Regular Cash or Credit r is the rate of inflation. If the price of a gallon of gas is currently $3.25, how long will it take for the price to rise to $4.00 if the Special 3.14% rate of inflation is 10.5%? 3.26% Super+ 3.36 Diesel 13. Population The population of a small coastal resort town, currently 3400, grows at a rate of 3% per year. This growth can be expressed by the exponential equation P = 3400(1 + 0.03) , where P is the population after t years. Find the number of years it will take for the population to reach 10,000.Solve each equation. Round your answers to the nearest ten-thousandth. 1) 8" = 76 2) 19" = 21.1 3) el = 47 4) 10" = 18 5) 9 . 10 = 8 6) 3* - 0.3 = 30 7) 15 + 3 =70 8) 3e = 60 9) 20 * = 31 10) eat = 68 11) 43* = 75 12) 13-20 = 2\f\f