Calculating Stem Length with Arithmetic Growth

This problem involves calculating the final length of a stem experiencing arithmetic growth. Arithmetic growth means the length increases by a constant amount over a specific period.

Understanding Arithmetic Growth

The formula for arithmetic growth is:

$L_t = L_0 + (r \times t)$

Where:

• $L_t$ is the length at time $t$.
• $L_0$ is the initial length at time $0$.
• $r$ is the constant arithmetic growth rate.
• $t$ is the time period.

Applying the Formula

We are given the following values:

• Initial length, $L_0 = 20\text{ cm}$
• Arithmetic growth rate, $r = 30\text{ cm}$ per day
• Time period, $t = 7$ days

First, calculate the total growth over the 7 days:

$ \text{Total Growth} = r \times t $

$ \text{Total Growth} = 30\text{ cm/day} \times 7\text{ days} = 210\text{ cm} $

Next, add the total growth to the initial length to find the final length:

$ L_7 = L_0 + \text{Total Growth} $

$ L_7 = 20\text{ cm} + 210\text{ cm} = 230\text{ cm} $

Final Stem Length

The length of the stem at the end of the $7^{\text{th}}$ day is $230\text{ cm}$.