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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.

Respuesta :

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.

[tex]\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[/tex]
sanchezmonica

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."

[tex]A=P(1+r)^{t}[/tex]

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

[tex]452=P(1+0.05)^{14}[/tex]

Then, we clear the variable P

[tex]P=\frac{452}{1.05^{14} }[/tex]

and perform the operations

[tex]P=\frac{452}{1.979931} =228.29centimeters[/tex]

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