Step 1 :The problem states that the plant grows by 16% per week. This means that each week, the plant's height is 116% of its height the previous week.
Step 2 :Therefore, the formula that represents the height of the tomato plant as a function of time would be the initial height of the plant multiplied by 1.16 raised to the power of the number of weeks since it was planted.
Step 3 :This corresponds to the formula \(h=9(1.16)^{t}\).
Step 4 :\(\boxed{h=9(1.16)^{t}}\) is the final answer.