SOLUTION: Find an exponential function of the form f(x) = ba−x + c that has the given horizontal asymptote and y-intercept and passes through point P. y = 34; y−intercept 659;

Algebra ->  Equations -> SOLUTION: Find an exponential function of the form f(x) = ba−x + c that has the given horizontal asymptote and y-intercept and passes through point P. y = 34; y−intercept 659;       Log On


   

Question 1156098: Find an exponential function of the form
f(x) = ba−x + c
that has the given horizontal asymptote and y-intercept and passes through point P.
y = 34; y−intercept 659; P(2, 134)
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Find an exponential function of the form
f%28x%29+=+ba%5E%28-x%29+%2B+c
that has the given horizontal asymptote and y-intercept and passes through point P.
y+=+34;
y-intercept 659;=> (0, 569)
A function of the form f%28x%29+=+a+%28bx%29+%2B+c+always has a horizontal asymptote at y+=+c
=> if given y+=+34, then c=34
f%28x%29+=+ba%5E%28-x%29+%2B34

use P(2, 134) and c=34

569+=+ba%5E-0+%2B+34
569+-34=+b+
b=535
so far
f%28x%29+=+535a%5E%28-x%29+%2B34.......=> use given point (2,134)
134=+535a%5E%28-2%29%2B34
134-34+=+535%2Fa%5E2+
100+=+535%2Fa%5E2+
a%5E2+=+535%2F100+
a%5E2+=+5.35+
a+=sqrt%28+5.35+%29
a=2.31301

your function is:

f%28x%29+=+535%282.31301%29%5E%28-x%29+%2B34




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


The other tutor made an ugly problem out of this by changing one of the numbers halfway through her work....

y+=+ba%5E%28-x%29%2Bc

(1) Horizontal asymptote y=34 means c=34.
y+=+ba%5E%28-x%29%2B34

(2) y-intercept 659 gives us the value of b:
659+=+b%28a%5E0%29%2B34
b+=+625

(3) Use the given point (2,134) to find a:
134+=+625a%5E%28-2%29%2B34
100+=+625a%5E%28-2%29
a%5E2+=+625%2F100
a+=+25%2F10+=+2.5

ANSWER: y+=+625%282.5%29%5E%28-x%29%2B34