Rewriting in $y=A_0\cdot e^{at}$ How do you rewrite $y = −8(1.589)^{t − 3}$ in $y=A_0e^{at}$ form for appropriate constants $A_0$ and $a?$
For other problems I took the $\ln$ of the number inside the parenthesis. So for example I would've done
$$y=-8\ln(1.589)^{t-3}$$
then I would get the answer 
$$y=-8(e^{0.46317-3})$$
but that is wrong on my assignment. What do I do with the $-3?$ I tried multiplying it by the $-8$ to get $24$ but that isn't right either. 

Note:  $(1.589)^{t-3}=(1.589)^t\cdot(1.589)^{-3}$.  Then you have
$$y=\frac{-8}{(1.589)^3}(1.589)^t$$
Now, also notice that $a=e^{\ln(a)}$.  Then this gives you
$$y=\frac{-8}{(1.589)^3}e^{\ln(1.589^t)}$$
Since $\ln(a^t)=t\ln(a)$, then we arrive at
$$y=\frac{-8}{(1.589)^3}e^{t\ln(1.589)}$$
where $a=\ln(1.589)$ and $A_0=\frac{-8}{(1.589)^3}$
