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The image shows a mathematical problem related to the growth of bamboo, represented by the equation \( L(t) = 3.5 \cdot t + 1150 \), where \( L(t) \) indicates the height of the bamboo stem in centimeters after \( t \) hours.

The tasks are:

**a) Bestem \( L(8) \):**
This requires calculating the height of the bamboo stem after 8 hours by substituting \( t = 8 \) into the equation.

**b) Løs ligningen \( L(t) = 1200 \), og forklar betydningen af løsningen:**
Solve the equation \( L(t) = 1200 \) for \( t \), and explain the meaning of the solution. Essentially, this asks when the bamboo will reach a height of 1200 cm.

**c) Forklar betydningen af tallene 3,5 og 1150 i forskriften:**
Explain the meaning of the constants 3.5 and 1150 in the equation. This requires interpreting these values in the context of the growth of the bamboo stem.

Let's solve each part.

### Part a: Bestem \( L(8) \)
Substitute \( t = 8 \) into the equation:

\[
L(8) = 3.5 \cdot 8 + 1150
\]

\[
L(8) = 28 + 1150 = 1178
\]

So, after 8 hours, the bamboo stem is **1178 cm tall**.

### Part b: Løs ligningen \( L(t) = 1200 \)
We need to solve for \( t \) when \( L(t) = 1200 \):

\[
1200 = 3.5 \cdot t + 1150
\]

Subtract 1150 from both sides:

\[
1200 - 1150 = 3.5 \cdot t
\]

\[
50 = 3.5 \cdot t
\]

Now, solve for \( t \) by dividing both sides by 3.5:

\[
t = \frac{50}{3.5} \approx 14.29
\]

So, it takes approximately **14.29 hours** for the bamboo to reach 1200 cm in height.

### Part c: Forklar betydningen af tallene 3,5 og 1150 i forskriften
- **3.5** represents the growth rate of the bamboo in centimeters per hour. This means that for every hour that passes, the bamboo grows by 3.5 cm.
- **1150** represents the initial height of the bamboo at time \( t = 0 \), which is 1150 cm.

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Would you like further details or explanations? 

Here are five questions to expand on this:

1. What would the height of the bamboo be after 24 hours?
2. How would the equation change if the initial height was different?
3. What happens to the growth if the rate changes from 3.5 to 5 cm per hour?
4. Can you model the growth after multiple days using this equation?
5. How would the equation change if the bamboo stopped growing after reaching a certain height?

**Tip:** To solve equations with multiple variables, always isolate the variable step by step!

The equation for bamboo growth is L(t) = 3.5 * t + 1150, where L(t) indicates the height of the bamboo stem in centimeters after t hours. The tasks are: a) Find L(8), b) Solve the equation L(t) = 1200 and explain the solution, and c) Explain the significance of the numbers 3.5 and 1150 in the formula.

Learn how to solve the bamboo growth equation L(t) = 3.5 * t + 1150 by calculating the height after 8 hours, solving for when the height reaches 1200 cm, and understanding the meaning of the constants 3.5 and 1150. Suitable for Grades 6-8.

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