Let's analyze the functions and the interval you provided. We have:

1. Functions:

   • $f(x) = 0.23x - 3$
   • $g(x) = 13(0.93^x)$

2. Interval:

   • $a = 15$
   • $b = 50$

If you’re interested in comparing the behavior of $f(x)$ and $g(x)$ over the interval $[15, 50]$, we can examine aspects such as intersection points, where one function is greater than the other, or specific values within that interval.

Key Steps

1. Intersection Points: Set $f(x) = g(x)$ and solve for $x$.
2. Comparison on $[15, 50]$: Find where $f(x) > g(x)$ and $f(x) < g(x)$.
3. Evaluate at Interval Boundaries: Check $f(a)$, $f(b)$, $g(a)$, and $g(b)$.

Would you like to proceed with any of these specific analyses?

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Questions for Further Exploration:

1. What is the solution for $f(x) = g(x)$ within the interval $[15, 50]$?
2. How does the growth of $g(x) = 13(0.93^x)$ compare to $f(x) = 0.23x - 3$ as $x$ increases?
3. What are the values of $f(x)$ and $g(x)$ at the endpoints $x = 15$ and $x = 50$?
4. On which parts of $[15, 50]$ is $f(x)$ greater than $g(x)$ and vice versa?
5. What are the maximum and minimum values of $f(x)$ and $g(x)$ on this interval?

Tip: For functions that grow or decay, like $g(x) = 13(0.93^x)$, observe the base of the exponential term to predict long