Nonlinear functions SAT question

The correct answer is $20$. It’s given that $f(x)=-a^x+b$. Substituting $-a^x+b$ for $f(x)$ in the equation $y=f(x)-12$ yields $y=-a^x+b-12$. It’s given that the y-intercept of the graph of $y=f(x)-12$ is $(0,-\frac{75}{7})$. Substituting $0$ for $x$ and $-\frac{75}{7}$ for $y$ in the equation $y=-a^x+b-12$ yields $-\frac{75}{7}=-a^0+b-12$, which is equivalent to $-\frac{75}{7}=-1+b-12$, or $-\frac{75}{7}=b-13$. Adding $13$ to both sides of this equation yields $\frac{16}{7}=b$. It’s given that the product of $a$ and $b$ is $\frac{320}{7}$, or $ab=\frac{320}{7}$. Substituting $\frac{16}{7}$ for $b$ in this equation yields $(a)(\frac{16}{7})=\frac{320}{7}$. Dividing both sides of this equation by $\frac{16}{7}$ yields $a=20$.