To solve [tex]\(\left(\frac{f}{g}\right)(4)\)[/tex], let's break it down step-by-step.
1. Define the functions:
- [tex]\( f(x) = 4x + 8 \)[/tex]: This represents the distance traveled by a herd of elephants in miles.
- [tex]\( g(x) = x - 1 \)[/tex]: This represents the time the herd traveled in hours.
2. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 4 \)[/tex]:
[tex]\[
f(4) = 4(4) + 8 = 16 + 8 = 24
\][/tex]
Hence, the distance traveled by the herd when [tex]\( x = 4 \)[/tex] is 24 miles.
3. Evaluate [tex]\( g(x) \)[/tex] at [tex]\( x = 4 \)[/tex]:
[tex]\[
g(4) = 4 - 1 = 3
\][/tex]
Hence, the time the herd traveled when [tex]\( x = 4 \)[/tex] is 3 hours.
4. Calculate [tex]\( \left(\frac{f}{g}\right)(4) \)[/tex]:
[tex]\[
\left(\frac{f}{g}\right)(4) = \frac{f(4)}{g(4)} = \frac{24}{3} = 8
\][/tex]
Hence, the value of [tex]\( \left(\frac{f}{g}\right)(4) \)[/tex] is 8.
5. Interpretation:
The ratio [tex]\(\left(\frac{f}{g}\right)(4) = 8\)[/tex] represents the elephants' rate in miles per hour. This means that when the herd has traveled for 4 hours, their average speed is 8 miles per hour.
Therefore, the correct interpretation is:
[tex]\[ \boxed{8; \text{ the elephants' rate in miles per hour}} \][/tex]
