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In our context, the percentage of adult height is a straightforward representation of how close a growing child is to reaching their mature stature. This method helps us understand growth progress using a mathematical function, like the one given in the problem:

• \(f(x) = 62 + 35 \log(x - 4)\)

This function uses logarithms to map out how a girl's height changes with age, between 5 and 15 years. By setting an age into the equation, it tells us what percentage of her adult height she has reached. For instance, at age 13, substituting \(x = 13\) in the function, we find \(f(13) \approx 95.4\). This means a 13-year-old girl has typically reached 95.4% of her adult height in this model, indicating most of her growth period is nearly complete by this age.

This insight helps understand both physical health and expected growth patterns during crucial development years.

Age modeling with functions like our logarithmic equation, \(f(x) = 62 + 35 \log (x-4)\), offers a powerful way to visualize growth over time. This model illustrates how someone ages, specifically how height percentage grows with increasing age from childhood to adolescence. Several factors make logarithmic functions a good fit for such models:

• They capture rapid early growth which then slows as maturity is approached.
• Logarithmic growth accurately portrays the diminishing returns in height gain as time progresses.

By plugging different values into the function for \(x\), representing varying ages, one can predict and analyze growth trends. This understanding is particularly useful, allowing parents and health professionals to plan and make informed observations about a child’s development. Monitoring such models can alert them to irregularities should a child's growth deviate from expected norms.

Simplifying functions is a key mathematical skill, allowing complex equations to become more understandable and solvable. The function here, \(f(x) = 62 + 35 \log(x - 4)\), underwent several simplification steps:1. **Substitution**: We first substitute the given age of 13 into the function, resulting in \(f(13) = 62 + 35 \log(13 - 4)\).
2. **Reduction**: Calculating inside the logarithm, the expression becomes \(\log(9)\), simplifying the equation to \(f(13) = 62 + 35 \log(9)\).3. **Calculation**: After finding the common log value, \(\log(9) \approx 0.95424\), it further simplifies to \(f(13) = 62 + 35 \times 0.95424\).4. **Finalizing**: Multiplying gives \(f(13) = 62 + 33.3984\), and upon adding, the answer \(f(13) = 95.4\) is rounded to the nearest tenth.
Through this simplification process, even complex expressions can be handled easily, making it possible to interpret results effectively.