|
Question 64216: 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).
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).
--------------------
f(x)=ba^x+c
f(x)=ba^x+c
If the horizontal asmptote is y=-2, c=-2
So, f(x)=ba^x-2
If the y-intercept is 2, f passes through (0,2)
So, 2=ba^0-2
4=b(1)
b=4
So, f(x)=4a^x-2
If the curve passes through (1,4),
4=4a^1-2
6=4a
a=3/2
FINALLY:
y=4(3/2)^x-2 is the equation you want.
Cheers,
Stan H.
|
|
|
| |
