Question 93114This question is from textbook Algebra and Trigonometry
: 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).
This question is from textbook Algebra and Trigonometry
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! 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).
Y=B(A^X)+C
Y INTERCEPT =2...THAT IS AT X=0...Y=2
2=B*(A^0)+C = B+C..................1
PASSES THROUGH (1,4).........Y=4 AT X=1
4=BA+C...................2
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
-2=B*0+C............3
C=-2
FROM EQN.1,WE GET
B-2=2
B=4
NOW FROM EQN.2
4=4A-2
A=6/4=1.5
HENCE EQN. IS
Y=4*(1.5)^X -2
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