Question 1084493: Write an exponential function in the form y=ab^x+c with asymptote y=-5, passing through points (0,1) and (2,31)
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The function has a horizontal asymptote at y=-5. If b>0, for large positive values of x, the function grows without bounds. For large negative values of x, the exponential term goes to zero, and the function approaches the value of c. Thus, c = -5.
The function is of the form y = ab^x - 5, and it passes through (0,1) and (2,31)
Thus 1 = ab^0 - 5 -> 1 = a - 5, or a = 6
31 = 6b^2 - 5 -> b^2 = 36/6, or b = sqrt(6)
Thus a function which satisfies the criteria is y = 6*(sqrt(6))^x - 5.
Or in a simpler form, since (6^(1/2))^x = 6^(x/2), we can write
y = 6^(x/2+1) - 5
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