If $\displaystyle{y}={a}{{b}}^{{x}}\usepackage{cmbright}\Huge\$ then when $\displaystyle{x}={0}\usepackage{cmbright}\Huge\$ , $\displaystyle{y}={a}\usepackage{cmbright}\Huge\$ . Since the table shows that $\displaystyle{y}={4}\usepackage{cmbright}\Huge\$ when $\displaystyle{x}={0}\usepackage{cmbright}\Huge\$ , then if the function is exponential, $\displaystyle{a}={4}\usepackage{cmbright}\Huge\$ so $\displaystyle{y}={4}{{b}}^{{x}}\usepackage{cmbright}\Huge\$ , which equals $\displaystyle{4}{b}\usepackage{cmbright}\Huge\$ when $\displaystyle{x}={1}\usepackage{cmbright}\Huge\$ , so $\displaystyle{4}{b}={8}\usepackage{cmbright}\Huge\$ and therefore b has to be 2. Since the equation $\displaystyle{y}={\left({4}\right)}{{2}}^{{x}}\usepackage{cmbright}\Huge\$ matches the information in the table, the function is exponential.