can someone help me with this problem..
well, I thought that f(x)= 2*e^(-x) was pretty close except when x at 2, y is not (2/9) but instead it's .5
any one can help?
thanks..
Well it goes through (0, 2), so
$\displaystyle 2 = Ca^0 \implies C = 2$
So the curve is $\displaystyle f(x) = 2a^x$.
Again, the curve goes through $\displaystyle \left ( 2, \frac{2}{9} \right ) $ so,
$\displaystyle \frac{2}{9} = 2a^2$
$\displaystyle \frac{1}{9} = a^2$
Thus
$\displaystyle a = \pm \frac{1}{3}$
Now, we may exclude the negative solution because the curve for this is, to put it mildly, psychotic. Thus
$\displaystyle f(x) = 2 \left ( \frac{1}{3} \right ) ^x$
-Dan