Compare the estimated average rate of change of the exponential function y=9(13)x and the quadratic function y=9x2 13x . Which function has a negative estimated average rate of change over the interval [0.1,0.6] ?(1 point) Responses both functions both functions the quadratic function the quadratic function the exponential function the exponential function neither function

Question

Compare the estimated average rate of change of the exponential function y=9(13)x and the quadratic function y=9x2 13x . Which function has a negative estimated average rate of change over the interval [0.1,0.6] ?(1 point) Responses both functions both functions the quadratic function the quadratic function the exponential function the exponential function neither function

Answer 1

To find the average rate of change of a function over an interval, we need to calculate the difference in the function values at the endpoints of the interval and divide by the difference in the input values.

For the exponential function y = 9(13)^x, the difference in function values is:
f(0.6) - f(0.1) = 9(13)^0.6 - 9(13)^0.1

And the difference in input values is:
0.6 - 0.1 = 0.5

Now let's find the average rate of change for the quadratic function y = 9x^2 + 13x. Again, the difference in function values is:
f(0.6) - f(0.1) = 9(0.6)^2 + 13(0.6) - (9(0.1)^2 + 13(0.1))

And the difference in input values is still 0.5.

Now we can compare the average rates of change for both functions.

If the average rate of change is positive, then the function is increasing over the interval.
If the average rate of change is negative, then the function is decreasing over the interval.

Based on the calculations, we can conclude that the quadratic function has a negative estimated average rate of change over the interval [0.1, 0.6]. Therefore, the correct answer is "the quadratic function".