Two weeks ago, Alice came home from vacation and noticed that a bean plant was growing in her garden. Today, the stalk is $452$ centimeters tall, and Alice observed that its height increases by $5\%$ every day.  How tall was the plant $2$ weeks ago when she first noticed it growing? Express your answer as a decimal to the nearest tenth.
Using a calculator, I get that $(1.05)^{14} \approx 1.979$. So the plant was $452 \div 1.979 \approx 228.3$ centimeters tall two weeks ago. 