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The problem involves a polynomial function modeling the height of a teak tree after \( x \) months, given by:

\[
h(x) = 0.5x^2 + 2x + 10
\]

**Questions:**
1. What is the height of the teak tree after 6 months?
2. How many months will it take for the tree to reach a height of 50 cm?

### Solution:

#### 1. Finding the height after 6 months:
Substitute \( x = 6 \) into the polynomial equation to find \( h(6) \):

\[
h(6) = 0.5(6^2) + 2(6) + 10
\]

#### 2. Finding when the height reaches 50 cm:
We set \( h(x) = 50 \) and solve for \( x \):

\[
0.5x^2 + 2x + 10 = 50
\]

Let me calculate the values.### 1. Height of the teak tree after 6 months:
\[
h(6) = 40 \, \text{cm}
\]

### 2. Time to reach 50 cm:
The tree will reach a height of 50 cm in approximately **7.17 months**. (We discard the negative solution of -11.17 months as it is not physically meaningful).

Would you like any further details or clarifications?

Here are 5 related questions:
1. How would the equation change if the tree grows faster over time?
2. What happens to the growth if an external factor slows it down?
3. How can we generalize this function to model different plants?
4. What if we wanted to find when the tree reaches 100 cm?
5. Can we model the tree's height beyond 12 months with this equation?

**Tip:** Polynomial functions like these are commonly used to model growth patterns that aren't linear but change with time.

Di sebuah sekolah adiwiyata, siswa menanam bibit pohon jati. Pertumbuhan tinggi pohon jati (dalam cm) setelah x bulan ditanam dapat dimodelkan dengan fungsi polinomial h(x) = 0.5x^2 + 2x + 10. Berapa tinggi pohon jati setelah 6 bulan? Berapa bulan yang dibutuhkan agar pohon jati mencapai tinggi 50 cm?

This math problem models the growth of a teak tree using a quadratic function. The solution covers calculating the height of the tree after 6 months and determining how long it takes for the tree to reach 50 cm. It involves key algebraic concepts, including solving quadratic equations.

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