12.How long will it take for an investment of $2550to double in value if the interest rate is 5.65%per year compounded continuously?Answer: 0.056551002550te0.05652te0.0565ln 2lnteln 212.270.0565t, about 12years, and 3months.13.[174]
5EXPONENTIAL AND LOGARITHMIC FUNCTIONS5.3Logarithmic FunctionsA sum of was invested for years, and the interest compounded quarterly. If this sum amounted to $6583.32in the given time, what was the interest rate?Answer: Use . Now solve for :4 86583.321250 14r325.2714r324ln5.27ln 1rln5.2732ln 14r0.0519ln 14r0.051914re0.213ror 21.3%14.Assume that the rat population in a certain urban area behaves according to the logistic growth function 0.312019tP tewhere Pis the number of rats in the hundreds, and tis measured in months.(a) Find the initial rat population.(b) Find the rat population after 1month.(c) After how many months will the rat population triple from its initial size?Answer: (a) 0.31 0200219Pe; 200rats(b) 0.31 12012.631219Pe, about 263rats(c)0.3120619te0.3120691te0.31739te0.31727te727ln4.40.31tmonths.15.For a rat learning to run a maze, the learning curve is given by 0.1108tS te, where S tis thetime it takes to run the maze in seconds after tdays. Use a graphing calculator or computer to graph ofthe learning curve and determine after how many days the rat is able to run the maze in 15seconds.Answer: 15S t0.115108te0.185te580.1lnt5810 ln4.7000t . So after 5days the rat can run the maze in 15seconds.[175]
5EXPONENTIAL AND LOGARITHMIC FUNCTIONS5.3Logarithmic Functions16.Use a graphing calculator to find all solutions of the equation 210log25xxcorrect to two decimal places.Answer: 1.61x17.Use a graphing calculator to find all solutions of the equation 3ln 32xxcorrect to two decimal places.Answer: 6.15x18.Use a graphing calculator to find all solutions of the equation 23323xxxcorrect to two decimalplaces.Answer: 3.50x 19.Solve the equation2log22100xxx.Answer: 10xor 1/10x.20.A 12-g sample of radioactive iodine decays in such a way that the mass remaining after t days is givenby 0.087( )12tm te, where ( )m tis measured in grams. After how many days is there only 4 gremaining?Answer: 13 days21.A 16-g sample of radioactive iodine decays in such a way that the mass remaining after t days is givenby 0.087( )16tm te, where ( )m tis measured in grams. After how many days is there only 4 gremaining?