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The problem presented in the image asks to find the function that describes height (\(H\)) as a function of age (\(A\)).

You are given the following dataThe problem presented in the image asks to find the function that describes height (\(H\)) as a function of age (\(A\)).

You are given the following 

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Alder (år)} & 6 & 8 & 10 & 12 & 14 \\
\hline
\text{Højde (cm)} & 119 & 132 & 143 & 155 & 167 \\
\hline
\end{array}
\]

### Step 1: Recognize the relationship
The height values seem to increase in a linear fashion. This suggests the relationship can be modeled by a linear function of the form:

\[
H(A) = mA + b
\]

Where:
- \(H(A)\) is the height in centimeters,
- \(A\) is the age in years,
- \(m\) is the slope (rate of change of height with respect to age),
- \(b\) is the y-intercept (height at age 0).

### Step 2: Calculate the slope
To find the slope (\(m\)), use two points from the table. Let's use the points \((6, 119)\) and \((8, 132)\):

\[
m = \frac{H_2 - H_1}{A_2 - A_1} = \frac{132 - 119}{8 - 6} = \frac{13}{2} = 6.5
\]

So, the slope \(m = 6.5\).

### Step 3: Find the intercept
To find \(b\), substitute one of the points (for example, \(A = 6\), \(H = 119\)) into the equation \(H = mA + b\):

\[
119 = 6.5(6) + b
\]
\[
119 = 39 + b
\]
\[
b = 119 - 39 = 80
\]

### Step 4: Write the final equation
The function that describes height as a function of age is:

\[
H(A) = 6.5A + 80
\]

This is the equation you're looking for.

Would you like more details or have any further questions?

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Here are 5 related questions that expand on this problem:

1. How would the function change if the growth rate (\(m\)) increased as age increases?
2. Can we use this function to predict the height at age 16? How accurate would that prediction be?
3. What if the data were non-linear? How would the approach to finding the function change?
4. How would we find the inverse of the function, representing age as a function of height?
5. How could we interpret the meaning of the y-intercept (\(b\)) in a real-world context?

**Tip**: Always check for linearity in a dataset by calculating the differences between consecutive values—this can give you an idea if a linear model is appropriate!

Bestem forskriften for funktionen, der beskriver højde som funktion af alder.

Learn how to find the linear function that describes height as a function of age using the given data points. This problem includes calculating the slope and intercept for a linear equation and is suitable for students in Grades 7-9.

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