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.

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

Answer 2

Answer:

Te plant was 228.29 centimeters tall.

Step-by-step 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

$P=\frac{452}{1.05^{14} }$

and perform the operations

$P=\frac{452}{1.979931} =228.29centimeters$