To solve these types of equations we use the following process. Pick an x value that is on the graph, solve each equation and see if the y value matches what is on the graph. If it does not, then it is not the answer. If it does, then it is a possible solution. If, you have more than one equation that was true after one point, you need to test another point.
Since we have a value for x=0 on the graph we will solve each equation for x=0 and see if the y value matches what is on the graph.
eqn 1. (0, 6) Does not match graph
eqn 2. (0, 4) Matches graph
eqn 3. (0, 2 3/4) Does not match graph
eqn 4. (0, 4) Matches graph
We see that #2 and #4 match the graph at x=0. So let's pick another x value. Say x = 2.
eqn 2.(2,16) Matches the graph
eqn 4.(2,1) Does not match the graph
Since only #2 matches when x=2 this must be our solution. f(x) = 4 * 2^x
