Answer
$f(x)=-40(1.025)^{x}$
Work Step by Step
Increasing x by 1 (from 1 to 2) ,
f(1) is multiplied by $\displaystyle \frac{-42.025}{-41}=1.025$ .
So, $ b=1.025,\qquad$and$ \quad f(x)=A(1.025)^{x}$
Now, given that $f(1)=-41,$
$-41=A(1.025)^{1}$
$\displaystyle \frac{-41}{1.025}=A$
$A=-40$
Thus,
$f(x)=-40(1.025)^{x}.$
