### Instruction: 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.### Response: I need to find the height of the plant $14$ days ago, which is the same as dividing its current height by the growth factor of $1.05$ raised to the power of $14$.
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.