Select the correct answer. Exponential function f is represented by the table. x & -1 & 0 & 1 & 2 & 3 & 4 f(x) & 80 & 26 & 8 & 2 & 0 & -(2)/(3) Function g is an exponential function passing through the points (0,7) and (3,0) . Which statement correctly compares the two functions on the interval (0,3) ? A. One function is positive on the interval, while the other is negative. B. Both functions are positive and increasing on the interval. C. Both functions are positive on the interval, but one function is increasing while the other is decreasin D. Both functions are positive and decreasing on the interval.

## Step 1: Analyze the function from the table### The function \( f(x) \) is given by the table with values at specific points. For the interval \( (0,3) \), we have:- \( f(0) = 26 \)- \( f(1) = 8 \)- \( f(2) = 2 \)- \( f(3) = 0 \)### Observing these values, \( f(x) \) is positive for and becomes zero at . Additionally, \( f(x) \) is decreasing as increases from 0 to 3.## Step 2: Analyze the exponential function ### Function is an exponential function passing through the points \( (0,7) \) and \( (3,0) \). Since it passes through \( (0,7) \), \( g(0) = 7 \), which is positive. At \( (3,0) \), \( g(3) = 0 \).### As \( g(x) \) is an exponential function that decreases from a positive value at to zero at , it must be positive and decreasing on the interval \( (0,3) \).## Step 3: Compare functions and on the interval \( (0,3) \)### Both functions and are positive on the interval \( (0,3) \) and both are decreasing as increases from 0 to 3.