Select the correct answer. Function f is an exponential function that has an initial value of 64 and decreases by 50% as x incre
ases by 1 unit. Function g is represented by the table. x 0 1 2 3 4 g(x) 75 43 27 19 15 Which statement correctly compares the two functions on the interval [0, 4]? A. Both functions are decreasing, but function f is decreasing at a faster average rate on that interval. B. Both functions are decreasing, but function g is decreasing at a faster average rate on that interval. C. Function f is decreasing, but function g is increasing, on that interval. D. Both functions are decreasing at the same average rate on that interval.
D. Both functions are decreasing at the same average rate on that interval
Step-by-step explanation:
The dashed lines on the attached graph of the two functions (f in red, g in purple) represent the average rate of change of each function on the interval. The lines are parallel, because the average rate of change is the same for each of the functions on that interval.
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Function f decreases by 60 units from f(0) = 64 to f(4) = 4 on the interval x = [0, 4]. Function g decreases by 60 units from g(0) = 75 to g(4) = 15 on the same interval. The average rate of change is the amount of decrease divided by the interval width. Those values are the same for both functions.
