Question

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.

Answer 1

so, on day 1, the plant was say "P" cm tall.

then 2 weeks go by, or 14 days, and the plant grew to 452 cm.


`\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to 452\\ P=\textit{initial amount}\\ r=rate\to 5\%\to (5)/(100)\to &0.05\\ t=\textit{elapsed time}\to &14\\ \end{cases} \\\\\\ 452=P(1+0.05)^(14)\implies \cfrac{452}{1.05^(14)}=P`

Answer 2

Te plant was 228.29 centimeters tall.

Explanation:

To find the size of the plant 14 days (2 weeks ago), we will use a formula called "exponential growth."

`A=P(1+r)^(t)`

where

A=accumulated amount.

P=initial ammount

r=rate

t=elapsed time.

replacing the values ​​we have

A=452 centimeters

P=variable to find

r=5% = 0.05

t=2 weeks= 14 days

So, we substitute the values ​​in the equation

`452=P(1+0.05)^(14)`

Then, we clear the variable P

`P=(452)/(1.05^(14) )`

and perform the operations

`P=(452)/(1.979931) =228.29centimeters`