SOLUTION: Find an exponential function of the form f(x) = ba^x that has the given y-intercept and passes through the point P. y-intercept 8; P(3, 1) I get 1/2 but my computer says

Algebra ->  Equations -> SOLUTION: Find an exponential function of the form f(x) = ba^x that has the given y-intercept and passes through the point P. y-intercept 8; P(3, 1) I get 1/2 but my computer says      Log On


   

Question 1155241: Find an exponential function of the form
f(x) = ba^x
that has the given y-intercept and passes through the point P.
y-intercept 8; P(3, 1)
I get 1/2 but my computer says it is wrong and I have redone the problem several times.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+ba%5Ex
given

y-intercept 8;=> is at point (0, 8)
P(3, 1)
recall that f%28x%29+=+y

f%28x%29+=+ba%5Ex....use point (0, 8)
8+=+ba%5E0
8+=+b%2A1.....solve for b
b=8........eq.1


f%28x%29+=+ba%5Ex....use point P(3, 1)
1+=+8a%5E3.....solve for a
a%5E3=1%2F8
a=root%283%2C1%2F8%29
a=root%283%2C1%2F2%5E3%29
a=1%2F2........eq.2

from eq.1 and eq.2 we have

f%28x%29+=+8%2A%281%2F2%29%5Ex



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


You say "I get 1/2".

What does that mean? The question asks for an exponential function; "1/2" is not a function.

What you found (apparently) was the a in the general form y=ba^x.

The a is 1/2; since the y-intercept (when x=0) is 8, the b in your function is 8.

The answer -- the exponential function -- is y=8(1/2)^x,