Math Problem Statement
Solution
The problem presented in the image asks to find the function that describes height () as a function of age ().
You are given the following dataThe problem presented in the image asks to find the function that describes height () as a function of age ().
You are given the following
\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$$ This is the equation you're looking for. Would you like more details or have any further questions? --- Here are 5 related questions that expand on this problem: 1. How would the function change if the growth rate ($$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!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Algebra
Slope and Intercept
Formulas
Linear function formula: H(A) = mA + b
Theorems
Slope calculation: m = (y2 - y1) / (x2 - x1)
Intercept calculation: b = y - mx
Suitable Grade Level
Grades 7-9
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