SOLUTION: Find an exponential function of the form f(x)=ba^-x+c that has the given horizontal asymptote and x and y-intercepts. y =-13; y-intercept 624; x-intercept 2

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find an exponential function of the form f(x)=ba^-x+c that has the given horizontal asymptote and x and y-intercepts. y =-13; y-intercept 624; x-intercept 2      Log On


   

Question 1145474: Find an exponential function of the form f(x)=ba^-x+c that has the given horizontal asymptote and x and y-intercepts. y =-13; y-intercept 624; x-intercept 2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
f%28x%29=ba%5E%28-x%29%2Bc
horizontal asymptote: y+=-13;
y-intercept 624;
x-intercept 2
If the horizontal asymptote is y=-13, we know that c=-13
so, we have: f%28x%29=ba%5E%28-x%29-13
If the y-intercept is 624, f passes through (0,624)
so, we have:
624=ba%5E%28-0%29-13
624%2B13=b%2A1
637=b
then we have:
f%28x%29=637a%5E%28-x%29-13
If the x-intercept is 2, f passes through (2,0), so we have

0=637a%5E%28-2%29-13
13=637%281%2Fa%5E2%29
13a%5E2=637
a%5E2=637%2F13
a%5E2=637%2F13
a%5E2+=+49
a=7
then we have:
f%28x%29=637%2A7%5E%28-x%29-13