Find values of a,b, and c for exponential function f(x) = cb^-x + a. Given that horizontal asymptote is y=72. Y-intercept is 425 and point P(1,248.5) lies on the graph.

Can anyone explain this step-by-step?

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- Nov 25th 2008, 12:04 PMmwokFinding values for a function with horizontal asymptote
Find values of a,b, and c for exponential function f(x) = cb^-x + a. Given that horizontal asymptote is y=72. Y-intercept is 425 and point P(1,248.5) lies on the graph.

Can anyone explain this step-by-step? - Nov 25th 2008, 12:30 PMskeeter
as x gets large, $\displaystyle cb^{-x}$ gets very small ... $\displaystyle a = 72$

y-intercept at $\displaystyle x = 0$ ... $\displaystyle cb^0 + 72 = 425$ ... $\displaystyle c = 353$

$\displaystyle x = 1$ ... $\displaystyle 248.5 = 353 \cdot b^{-1} + 72$

you solve for $\displaystyle b$.