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
A. the exponential function
B. both functions
C. the quadratic function
D. neither function
To find the estimated average rate of change of a function over an interval, we can use the formula:
Average rate of change = (f(b) - f(a))/(b - a)
For the exponential function y = 9(13)^x, the estimated average rate of change over the interval [0.1, 0.6] would be:
(f(0.6) - f(0.1))/(0.6 - 0.1) = (9(13)^0.6 - 9(13)^0.1)/(0.5)
Simplifying further, we get:
(f(0.6) - f(0.1))/(0.6 - 0.1) = (9(13)^0.6 - 9(13)^0.1)/(0.5) ≈ 26.847
For the quadratic function y = 9x^2 + 13x, the estimated average rate of change over the interval [0.1, 0.6] would be:
(f(0.6) - f(0.1))/(0.6 - 0.1) = (9(0.6)^2 + 13(0.6) - (9(0.1)^2 + 13(0.1))/(0.5)
Simplifying further, we get:
(f(0.6) - f(0.1))/(0.6 - 0.1) = (9(0.6)^2 + 13(0.6) - (9(0.1)^2 + 13(0.1))/(0.5) ≈ 3.66
Comparing the estimated average rate of change of the two functions:
- The exponential function has an estimated average rate of change of approximately 26.847
- The quadratic function has an estimated average rate of change of approximately 3.66
Since the estimated average rate of change of the exponential function is positive and the estimated average rate of change of the quadratic function is positive, the correct answer is:
D. neither function