document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012078>Question 1012078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For each exponential function, state the domain and range, whether the function increases or decreases, and the y-intercept.\r<BR>\n" );
document.write( "\n" );
document.write( "a) y=2(4)^x<BR>\n" );
document.write( "b) y=3(1/2)^x<BR>\n" );
document.write( "c) y=-(0.3)^x<BR>\n" );
document.write( "d) y=-3(5.2)^x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627948 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627948\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> in all of these, the domain is all real values of x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the range and the y-intercept for each is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a) y=2(4)^x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the range is all real value of y > 0.<BR>\n" );
document.write( "the y-intercept is y = 2 * 4^0 = 2*1 = 2.<BR>\n" );
document.write( "the function is increasing form left to right.<BR>\n" );
document.write( "that's the red equation in the graph shown below.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b) y=3(1/2)^x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the range is all real values of y > 0.<BR>\n" );
document.write( "the y-intercept is y = 3 * (1/2)^0 = 3 * 1 = 3.<BR>\n" );
document.write( "the function is decreasing from left to right.<BR>\n" );
document.write( "that's the blue equation in the graph shown below.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c) y=-(0.3)^x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the range is all real values of y < 0.<BR>\n" );
document.write( "the y-intercept is equal to -(0.3)^0 = -1.<BR>\n" );
document.write( "the graph is increasing from left to right.<BR>\n" );
document.write( "that's the green equation in the graph shown below.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d) y=-3(5.2)^x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the range is all real values of y < 0.<BR>\n" );
document.write( "the y-intercept is equal to -3 * (5.2)^0 = -3 * 1 = -3.<BR>\n" );
document.write( "the graph is decreasing from left to right.<BR>\n" );
document.write( "that's the purple equation in the graph shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "see below the graph for further comments.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/010301.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2*4^x is increasing because, as x gets larger, 4^x gets larger.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3*(1/2)^x is decreasing because, as x gets larger, (1/2)^x gets smaller.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(1/2)^1 = 1/2<BR>\n" );
document.write( "(1/2)^2 = 1/4<BR>\n" );
document.write( "etc.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-.3^x is increasing because, as x gets larger, .3^x gets smaller and so minus .3^x gets larger.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".3^1 = .3<BR>\n" );
document.write( ".3^2 = .09<BR>\n" );
document.write( ".09 is smaller than .3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-.3^1 = -.3<BR>\n" );
document.write( "-.3^2 = -.09<BR>\n" );
document.write( "-.09 is larger than -.3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-3*5.2^x is decreasing because, as x gets larger, 5.2^x gets larger and so minus 5.2^x gets smaller.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5.2^1 = 5.2<BR>\n" );
document.write( "5.2^2 = 27.04<BR>\n" );
document.write( "27.04 is larger than 5.2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-5.2^1 = -5.2<BR>\n" );
document.write( "-5.2^2 = -27.04<BR>\n" );
document.write( "-27.04 is smaller than -5.2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );