StewartCalcETPPT学习教案

1、会计学1StewartCalcETCopyright Cengage Learning. All rights reserved. Exponential Functions第1页/共36页第2页/共36页5?第3页/共36页.nWe want to fill in the holes by defining f(x) = 2x, wherex , so that f is an increasing function.Figure 1Representation of y = 2x, x rational第4页/共36页第5页/共36页第6页/共36页compute it correct t

2、o six decimal places:第7页/共36页Figure 2y = 2x, x realFigure 1Representation of y = 2x, x rational第8页/共36页Figure 3第9页/共36页basically three kinds of exponential functions y= bx. nIf 0 b 1, it increases.第10页/共36页Figure 4(b) y = 1x(a) y = bx, 0 b 1第11页/共36页第12页/共36页第13页/共36页Figure 5(a) y = 2x(b) y = 2xFigu

3、re 2y = 2x, x real第14页/共36页nThe domain is and the range is ( , 3).Figure 5(c) y = 3 2xcontd第15页/共36页Applications of Exponential Functions第16页/共36页第17页/共36页np(t) = 2t 1000 = (1000)2t第18页/共36页第19页/共36页Figure 8Scatter plot for world population growth第20页/共36页data points.Figure 9Exponential model for po

4、pulation growth第21页/共36页第22页/共36页mass to be reduced to 5 mg.第23页/共36页第24页/共36页contd第25页/共36页nmto estimate that m(t) = 5 when t 57. So the mass of the sample will be reduced to 5 mg after about 57 years.contdFigure 12第26页/共36页The Number e第27页/共36页第28页/共36页tangent line to an exponential graph at a poi

5、nt as the line that touches the graph only at that point.) If we measure the slopes of these tangent lines at (0, 1), we find that m 0.7 for y = 2x and m 1.1 for y = 3x.Figure 14Figure 13第29页/共36页Figure 15The natural exponential function crosses the y-axis with a slope of 1.第30页/共36页第31页/共36页Figure 16Figure 14Figure 13第32页/共36页第33页/共36页Figure 17(b) y = ex(a) y = exFigure 15The natural exponential functioncrosses the y-axis wit