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All Textbook Solutions for Trigonometry (MindTap Course List)
2ECPEstimate the age of a newly discovered fossil for which the ratio of carbon-14 to carbon-12 is R=1/1014.4ECP5ECPFind the intensities of earthquakes whose magnitudes are aR=6.0andbR=7.9.1E2E3E4E5E6E7E8E9E10E11E12E13E14ECompound Interest In Exercises 15 and16, determine the time necessary for P dollars to double when it is invested at interest rate r compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. r=1016E17E18E19E20E21E22E23E24E25E26E27E28E29EPopulation The table shows the mid-year populations (in millions) of five countries in 2015 and the projected populations (in millions) for the year 2025. (a) Find the exponential growth or decay model y=aebt or y=aebt for the population of each country by letting t=15 correspond to 2015. Use the model to predict the population of each country in 2035. (b) You can see that the populations of the United States and the United Kingdom are growing at different rates. What constant in the equation y=aebt gives the growth rate? Discuss the relationship between the different growth rates and the magnitude of the constant.31E32E33E34EDepreciation A laptop computer that costs $575 new has a book value of $275 after 2 years. (a) Find the linear model V=mt+b. (b) Find the exponential model V=aekt. (c) Use a graphing utility to graph the two models in the same viewing window. Which model depreciates faster in the first 2 years? (d) Find the book values of the computer after 1 year and after 3 years using each model. (e) Explain the advantages and disadvantages of using each model to a buyer and a seller.36E37ECarbon Dating The ratio of carbon-14 to carbon-12 in a piece of paper buried in a tomb is R=1/1311. Estimate the age of the piece of paper.39EEducation The amount of time (in hours per week) a student utilizes a math-tutoring center roughly follows the normal distribution y=0.7979ex5.42/0.5,4x7 where x is the number of hours. (a) Use a graphing utility to graph the function. (b) From the graph in part (a), estimate the average number of hours per week a student uses the tutoring center.41E42E43E44E45E46E47E48E49E50E51E52E53E54EpH Levels In Exercises 5156, use the acidity model pH=logH+, where acidity pH is a measure of the hydrogen ion concentration H+ (measured in moles of hydrogen per liter) of a solution. Apple juice has a pH of 2.9 and drinking water has a pH of 8.0. The hydrogen ion concentration of the apple juice is how many times the concentration of drinking water?56EForensics At 8:30 A.M., a coroner went to the home of a person who had died during the night. In order to estimate the time of death, the coroner took the person’s temperature twice. At 9:00 A.M. the temperature was 85.7F, and at 11:00 A.M. the temperature was 82.8F. From these two temperatures, the coroner was able to determine that the time elapsed since death and the body temperature were related by the formula t=10lnT7098.670 where t is the time in hours elapsed since the person died and T is the temperature (in degrees Fahrenheit) of the person’s body. (This formula comes from a general cooling principle called Newton’s Law of Cooling. It uses the assumptions that the person had a normal body temperature of 98.6F at death and that the room temperature was a constant 70F.) Use the formula to estimate the time of death of the person.58E59E60E61E62E63E64EHOW DO YOU SEE IT? Identify each model as exponential growth, exponential decay, Gaussian, linear, logarithmic, logistic growth, quadratic, or none of the above. Explain your reasoning.Evaluating an Exponential Function In Exercises 16, evaluate the function at the given value of x. Round your result to three decimal places. fx=0.3x,x=1.52RE3RE4RE5RE6RE7RE8RE9RE10RE11RE12RE13RE14RE15RE16RE17RE18RE19RE20RE21RE22RE23RE24RE25RE26RE27RE28RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48RE49RE50RE51RE52RE53RE54RE55RE56RE57RE58RE59RE60RE61RE62RE63REUsing Properties of Logarithms In Exercises 63-66, use the properties of logarithms to write the logarithm in terms of log23 and log25. log24565RE66RE67RE68RE69RE70RE71RE72RE73RE74RE75RE76RE77RE78RE79RE80RE81RE82RE83RE84RE85RE86RE87RE88RE89RE90RE91RE92RE93RE94RE95RE96RE97RE98RE99RE100RE101RE102RE103RE104RE105RE106RE107RE108RE109RE110RE111RE112RE113RE114RE115RE116RE117RE118RE1T2T3T4T5T6T7T8T9T10T11TIn Exercises 12-14, evaluate the logarithm using the change-of-base formula. Round your result to three decimal places. log53513T14T15T16T17TIn Exercises 18-20, condense the expression to the logarithm of a single quantity. log313+log3yIn Exercises 18-20, condense the expression to the logarithm of a single quantity. 4lnx4lny20T21T22T23T24T25T26T27T28T29T1PS2PS3PS4PS5PS6PS7PS8PS9PS10PS11PS12PS13PS14PS15PS16PS17PS18PS19PSFinding Slope and y-Intercept Take the natural log of each side of each equation below. y=abx,y=axb (a) What are the slope and y-Intercept of the line relating x and lny for y=abx? (b) What are the slope and y-Intercept of the line relating lnx and lny for y=axb?21PS22PS23PS24PS25PS26PSFind the inclination of (a) 4x5y=7 and (b) x+y=1.2ECP3ECPFind the distance between the point 3,2 and the line 3x+5y=2.5ECP1E2E3E4E5E6E7E8EFinding the Slope of a Line In Exercises 5-16 find the slope of the line with inclination . =3radiansFinding the Slope of a Line In Exercises 5-16 find the slope of the line with inclination . =56radians11EFinding the Slope of a Line In Exercises 5-16, find the slope of the line with inclination . =0.63radianFinding the Slope of a Line In Exercises 5-16, find the slope of the line with inclination . =1.27radians14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29EFinding the Inclination of a Line In Exercises 2534, find the inclination (in radians and degrees) of the line passing through the points. 12,8,4,331E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48E49E50E51E52E