Question

Find the equation of the following exponential, using the form a(b)^x

I keep getting this wrong because I don't know what points to use for the equation

Answer 1

Check the picture below.

$f(x)=ab^x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know that}}{x=0\qquad f(x)=-1}\qquad -1=ab^0\implies -1=a(1) \\\\\\ -1=a ~\hfill \underline{f(x)=-1b^x} \\\\\\ \stackrel{\textit{we also know that}}{x=1\qquad f(x)=-4}\qquad -4=-1b^1\implies \cfrac{-4}{-1}=b^1 \\\\\\ 4=b ~\hfill \underline{f(x)=-4^x}$