Clever people on this place, I'm having trouble with this, and I'm not able to see why what I'm doing is wrong... Here are two points:
$(3,1)$, $(-1,16)$
And this is what my calculations are:
First, I'll find $a$:
$ a = (x_2-x_1)\sqrt{\frac{y2}{y1}}= (-1 + (-3) )\sqrt{\frac{16}{1}}\\\Leftrightarrow \\a = -4\sqrt{\frac{16}{1}}n \\\Leftrightarrow \\a = -4\sqrt{\frac{16}{1}} \Rightarrow a=−16 $
Then, I can find $b$:
$b = (\frac{y1}{a^x1}))= \frac{1}{-16^3}\\ \Rightarrow b=−0.000244$
This is wrong, my book says that the answer is $f(x) = 8(2^{-x})$
What's wrong, and what should be changed here? I'm not the biggest math professor, but i hope you can help me aswell.
What i need to know is how the final function can be, as it says in the book - in this case, it's $f(x) = a (b^x)$