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Exponential function f is represented by the table.

x 0 1 2 3 4
f(x) 15 7 3 1 0

Function g is an exponential function passing through the points (0,9) and (3,0).

Which statement correctly compares the two functions?

A.
Both functions are decreasing on [0, 3], and function g is decreasing at a faster rate.
B.
Only function g is decreasing on [0, 3], and only function f is positive on that interval.
C.
Only function f is decreasing on [0, 3], and both functions are positive on that interval.
D.
Both functions are decreasing on [0, 3], and function f is decreasing at a faster rate.

Answer :

Considering the given exponential functions, it is found that the correct statement is:

D. Both functions are decreasing on [0, 3], and function f is decreasing at a faster rate.

What is the behavior of each exponential function?

  • For function f, we have that it is decreasing, as it is greater at x = 0 than at x = 4, and it decreases by an average of 3.75 units when the input changes by 1.
  • For function g, we also have that it is decreasing, as as it is greater at x = 0 than at x = 3, and it decreases by an average of 3 units when the input changes by 1.

Hence option D is correct.

More can be learned about exponential functions at https://brainly.com/question/25537936

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