Jeff plants a 9-inch tomato plant in his garden. The plant grows by about $16 \%$ per week for several months. Which formula represents the height $h$ of the tomato plant (in inches) as a function of the time $t$ in weeks since it was planted?
$h=9(0.16)^{t}$
$h=9(1.16)^{t}$
$h=9(1.16 t)$
$h=9+0.16 t$
$h=9+1.16 t$
Answer
\(\boxed{h=9(1.16)^{t}}\) is the final answer.
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.
