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Select the correct answer.
Function f is an exponential function that has an initial value of 64 and decreases by 50% as x increases 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]?
O A. Both functions are decreasing, but function f is decreasing at a faster average rate on that interval.
O B.
C.
D.
Function f is decreasing, but function g is increasing, on that interval.
Both functions are decreasing at the same average rate on that interval.
Both functions are decreasing, but function g is decreasing at a faster average rate on that interval.

Respuesta :

Answer:

Certainly! Let’s compare the two functions, f and g, on the interval ([0,4]).

Function f:

It is an exponential function with an initial value of 64.

It decreases by 50% as x increases by 1 unit.

The general form of f(x) is: (f(x) = 64 \cdot (0.5)^x).

Function g:

It is represented by the given table:

X   g(x)

0   75

1   43

2   27

3   19

4   15

We can observe that g(x) is decreasing as x increases.

Now let’s compare the average rates of decrease for both functions:

Function f:

Initial value: (f(0) = 64)

Final value at (x = 4): (f(4) = 64 \cdot (0.5)^4 = 4)

Average rate of decrease: (\frac{{f(0) - f(4)}}{4} = \frac{{64 - 4}}{4} = 15)

Function g:

Initial value: (g(0) = 75)

Final value at (x = 4): (g(4) = 15)

Average rate of decrease: (\frac{{g(0) - g(4)}}{4} = \frac{{75 - 15}}{4} = 15)

Since both functions have the same average rate of decrease on the interval ([0,4]), the correct statement is:

C. Both functions are decreasing at the same average rate on that interval.

If you have any more questions or need further clarification, feel free to ask!

Step-by-step explanation:

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