x & f(x) 0 & 100 1 & 120 2 & 144 3 & 172.8

## Step 1: Observing the given valuesWe are given a table with two columns, where the left column represents values of and the right column represents corresponding values of a function \(f(x)\).- When , \(f(x) = 100\).- When , \(f(x) = 120\).- When , \(f(x) = 144\).- When , \(f(x) = 172.8\).## Step 2: Identifying the pattern- The value of \(f(x)\) increases as increases.- The ratio of consecutive \(f(x)\) values seems consistent. To confirm this, we calculate the ratio of each pair of consecutive values:- - - - This consistent ratio suggests that the function \(f(x)\) could be an exponential function where each step involves multiplying by a constant factor, in this case, 1.2.## Step 3: Formulating the function- Given the pattern, the function can be expressed as \(f(x) = 100 \times 1.2^x\). This formula fits all the given data points.## Step 4: Verifying the function- For , \(f(0) = 100 \times 1.2^0 = 100\).- For , \(f(1) = 100 \times 1.2^1 = 120\).- For , \(f(2) = 100 \times 1.2^2 = 144\).- For , \(f(3) = 100 \times 1.2^3 = 172.8\).- The function \(f(x) = 100 \times 1.2^x\) correctly produces all the values in the table.## Step 5: Conclusion- The function \(f(x)\) is an exponential function where the base value is 100, and it is multiplied by 1.2 for each increase in by 1.