document.write( "Question 93114This question is from textbook Algebra and Trigonometry
\n" ); document.write( ": Find an exponential function of the form f(x)=ba^x+c with y-intercept 2, horizontal asymptote y=-2, that passes through the point P(1,4). \n" ); document.write( "
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Find an exponential function of the form f(x)=ba^x+c with y-intercept 2, horizontal asymptote y=-2, that passes through the point P(1,4).
\n" ); document.write( "Y=B(A^X)+C
\n" ); document.write( "Y INTERCEPT =2...THAT IS AT X=0...Y=2
\n" ); document.write( "2=B*(A^0)+C = B+C..................1
\n" ); document.write( "PASSES THROUGH (1,4).........Y=4 AT X=1
\n" ); document.write( "4=BA+C...................2
\n" ); document.write( "HORIZONTAL ASYMPTOTE IS Y=-2......THAT IS AS X TENDS TO + OR - INFINITY,Y TENDS TO -2...HERE WE TAKE X TENDING TO -INFINITY AS OTHERWISE , A^X WILL BE INFINITE.HENCE
\n" ); document.write( "-2=B*0+C............3
\n" ); document.write( "C=-2
\n" ); document.write( "FROM EQN.1,WE GET
\n" ); document.write( "B-2=2
\n" ); document.write( "B=4
\n" ); document.write( "NOW FROM EQN.2
\n" ); document.write( "4=4A-2
\n" ); document.write( "A=6/4=1.5
\n" ); document.write( "HENCE EQN. IS
\n" ); document.write( "Y=4*(1.5)^X -2 \n" ); document.write( "
\n" );