# More formula stuff...

• Aug 28th 2009, 01:29 PM
JAMESveeder
More formula stuff...
Ok, so I'm pretty darn sure I'm not setting these up right.

Saturated growth can be modeled by P(t) = S - Se-kx. Find the exact values of S and k for the graph below if the horizontal asymptote is y = 9 and the indicated point is (1, 7)

How would I even begin to set this up?
• Aug 28th 2009, 02:30 PM
skeeter
Quote:

Originally Posted by JAMESveeder
Ok, so I'm pretty darn sure I'm not setting these up right.

Saturated growth can be modeled by P(t) = S - Se-kx. Find the exact values of S and k for the graph below if the horizontal asymptote is y = 9 and the indicated point is (1, 7)

How would I even begin to set this up?

I think you mean ...

$P(t) = S - Se^{-kt} = S(1 - e^{-kt})$

$\lim_{t \to \infty} S(1 - e^{-kt}) = 9$ indicates $S = 9$ since $e^{-kt}$ approaches 0 as t gets large.

$P(1) = 7$

$7 = 9(1 - e^{-k})$

solve for $k$