Question

I need to find an initial value, rate of change, and a domain from a graph

Answer 1

`\begin{gathered} f(x)=ab^x \\ \text{for (}0,1\text{)} \\ 1=ab^0 \\ 1=a(1) \\ a=1 \\ \text{for (}1,(1)/(3)\text{)} \\ (1)/(3)=(1)b^1 \\ \\ (1)/(3)=b \\ The\text{ base is }(1)/(3) \\ f(x)=1\cdot((1)/(3))^x \\ f(x)=((1)/(3))^x \\ The\text{ domain is all real numbers or (-}\infty,\infty\text{)} \end{gathered}`