44.y5}11510.12x}111.12x5}5y0}1.12x5}5y0}21log1.1(1.12x)5log1.11}5y0}2122x5log1.11}5y0}212x5 2log1.11}5y0}2125 2log1.11}50y2y}25log1.11}50y2y}2Interchange xand y:y5log1.11}50x2x}2f21(x)5log1.11}50x2x}2Verify.(f +f21)(x)5f1log1.11}50x2x}225555}x1(5500x2x)}5}5500x}5x(f21+f)(x)5f211}11510.12x}25log1.1125log1.1125log1.11}1.112x}25log1.1(1.1x)5x45. (a)f(f(x))5ˇ1w2w(wf(wx)w)2w5ˇ1w2w(w1w2wxw2)w5ˇx2w5)x)5x, sincex $0(b)f(f(x))5f1}1x}25}11/x}5xfor all x046. (a)Amount 581}12}2t/12(b)81}12}2t/12511}12}2t/125}18}1}12}2t/1251}12}23}1t2}53t536There will be 1 gram remaining after 36 hours.47.500(1.0475)t510001.0475t52ln(1.0475t)5ln 2tln 1.04755ln 2t5}ln 1ln.02475}<14.936It will take about 14.936 years. (If the interest is paid at theend of each year, it will take 15 years.)48.375,000(1.0225)t51,000,0001.0225t5}83}ln(1.0225t)5ln1}83}2tln 1.02255ln1}83}2t5}lnln1(.80/232)5}<44.081It will take about 44.081 years.49. (a)y5 22539.8521636.896 ln x(b)When x575,y <209.94. About 209.94 million metrictons were produced.
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