Question 50264: Need some help with this one.
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).
Found 2 solutions by Nate, stanbon:
Answer by Nate(3500)   (Show Source):
You can put this solution on YOUR website! f(x) = ba^x + c
y = ba^x - 2
y = ba^x - 2 P(0,2)
2 = ba^0 - 2
2 = b - 2
4 = b
plug.:
y = 4*a^x - 2 P(1,4)
4 = 4*a - 2
6 = 4a
3/2 = a
plug.:
f(x) = 4(3/2)^x - 2
Answer by stanbon(75887) (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=ba^x+c
Since horizontal asymptote = -2, c=-2
y=ba^x-2
Since the y-intercept is 2,
2=b(1)-2
b=4
y=4a^x-2
Since it passes through (1,4)
4=4a^1-2
6=4a
a=(3/2)
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EQUATION: y=4(3/2)^x-2
Cheers,
Stan H.
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