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Question 47998: Find the 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).
Possible solutions are:
a. f(x)=-2(2^x)
b. f(x)=2(2^x)-2
c. f(x)=2(1.5^x)-2
d. f(x)=4(1.5^x)-2
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the 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-intercept 2 means it passes through (0,2)
Then 2=ba^0 + c
2=b+c
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horizontal asymptote y=-2 means c=-2
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Substitute that into 2=b+c to get
2=b-2
b=4
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Passes through the point (1,4) means
4=a(4^1)-2
6=4a
a=(3/2)
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EQUATION:
y=4(3/2)^x -2
That is answer "d"
Cheers,
Stan H.
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