Question: Select the correct answer. Exponential function $f$ is represented by the table. $x$ 0 1 2 3 4 $f(x)$ 868 292 148 112 103 Function $g$ is an exponential function passing through the points $(0,800)$ and $(4,0)$. Which statement correctly compares the two functions? Both functions are decreasing on $[0, 4]$, but function $g$ decreases at a faster rate. Only function $g$ is decreasing on $[0, 4]$, and only function $f$ is positive on that interval. Only function $f$ is decreasing on $[0, 4]$, and both functions are positive on that interval. Both functions are decreasing on $[0, 4]$, but function $f$ decreases at a faster rate.

1. **State the problem:** We have two exponential functions $f$ and $g$ defined on the interval $[0,4]$. Function $f$ is given by a table of values, and function $g$ passes through points $(0,800)$ and $(4,0)$. We need to compare their behavior on $[0,4]$. 2. **Analyze function $f$:** From the table, $f(0)=868$, $f(1)=292$, $f(2)=148$, $f(3)=112$, $f(4)=103$. The values decrease as $x$ increases, so $f$ is decreasing on $[0,4]$. Also, all values are positive. 3. **Analyze function $g$:** It passes through $(0,800)$ and $(4,0)$. Since $g(4)=0$, the function reaches zero at $x=4$. Because exponential functions are either always positive or always zero, and $g$ reaches zero, it must be decreasing on $[0,4]$ to go from $800$ to $0$. However, $g$ is not positive on the entire interval since it reaches zero at $x=4$. 4. **Compare rates of decrease:** - For $f$, the ratio $\frac{f(1)}{f(0)}=\frac{292}{868}\approx0.336$. - For $g$, the function goes from $800$ to $0$ in 4 units, which is a faster decrease than $f$. 5. **Conclusion:** Both functions decrease on $[0,4]$, but $g$ decreases faster. Also, $f$ remains positive, but $g$ reaches zero. **Final answer:** Both functions are decreasing on $[0, 4]$, but function $g$ decreases at a faster rate.