SOLUTION: Find an exponential function of the form f(x) = C · a^x + D with horizontal asymptote y =1 whose graph contains the points (1,7)and (0,5).

Algebra ->  Exponents -> SOLUTION: Find an exponential function of the form f(x) = C · a^x + D with horizontal asymptote y =1 whose graph contains the points (1,7)and (0,5).      Log On


   

Question 1153466: Find an exponential function of the form f(x) = C · a^x + D with horizontal asymptote y =1 whose graph contains the points (1,7)and (0,5).
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Horizontal asymptote at y=1:

For a pure exponential function (D=0), the horizontal asymptote is 0. For the horizontal asymptote to be 1, D must be 1.

f%28x%29+=+C%2Aa%5Ex%2B1

The function value at x=0 is 5:

5+=+C%2Aa%5E0%2B1
5+=+C%2B1
C+=+4

f%28x%29+=+4%28a%5Ex%29%2B1

The function value at x=1 is 7:

7+=+4%28a%5E1%29%2B1
7+=+4a%2B1
6+=+4a
a+=+1.5

f%28x%29+=+4%281.5%29%5Ex%2B1

A graph:

graph%28600%2C400%2C-10%2C5%2C-2%2C12%2C4%281.5%29%5Ex%2B1%29