Remember that an exponential function takes the form [tex]b \cdot a^x[/tex]. We can see that the problem additionally gave us two points on the curve, which means that we can make two equations in attempt to find [tex]a[/tex]. (This is done by using the x-values and y-values that the points on the graph show, and substituting them into the general form.)
[tex]b \cdot a^0 = b = 5[/tex]
[tex]b \cdot a^1 = 7[/tex]
Substituting the value we found for [tex]b[/tex] that we found in the first equation into the second equation, we can create a better equation and solve for [tex]a[/tex].
[tex]5 \cdot a = 7[/tex]
[tex]a = \dfrac{7}{5}[/tex]
Now, we have found [tex]b = 5[/tex] and [tex]a = \dfrac{7}{5}[/tex], which means that we can create the final curve.
[tex]\boxed{y = 5 \cdot \Big( \dfrac{7}{5} \Big)^x}[/tex]
