Question

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?

A.
Both functions are decreasing on [0, 4], but function f decreases at a faster rate.
B.
Only function f is decreasing on [0, 4], and both functions are positive on that interval.
C.
Both functions are decreasing on [0, 4], but function g decreases at a faster rate.
D.
Only function g is decreasing on [0, 4], and only function f is positive on that interval.

Answer 1

C

Both are decreasing on [0,4]. f falls from 868 to 103 (a drop of 765 over 4 units, average −191.25 per unit), while g falls from 800 to 0 (a drop of 800 over 4 units, average −200 per unit), so g decreases at a slightly faster rate.