Question
Compare the estimated average rate of change of the exponential function y=9(1/3)x and the quadratic function y=9x2+1/3x. Which function has a negative estimated average rate of change over the interval [0.1,0.6] ?
neither function
both functions
the exponential function
the quadratic function
neither function
both functions
the exponential function
the quadratic function
Answers
GPT 3.5
To find the estimated average rate of change for each function over the interval [0.1,0.6], we need to calculate the change in y divided by the change in x.
For the exponential function, y = 9(1/3)^x, we have:
f(0.1) = 9(1/3)^0.1 ≈ 7.311
f(0.6) = 9(1/3)^0.6 ≈ 2.383
Estimated average rate of change = (2.383 - 7.311) / (0.6 - 0.1) = - 0.973
For the quadratic function, y = 9x^2 + (1/3)x, we have:
f(0.1) = 9(0.1)^2 + (1/3)(0.1) = 0.093
f(0.6) = 9(0.6)^2 + (1/3)(0.6) = 3.54
Estimated average rate of change = (3.54 - 0.093) / (0.6 - 0.1) = 7.894
Since the estimated average rate of change for the exponential function is negative (-0.973) and the estimated average rate of change for the quadratic function is positive (7.894), the exponential function has a negative estimated average rate of change over the interval [0.1,0.6].
Therefore, the correct answer is: the exponential function.
For the exponential function, y = 9(1/3)^x, we have:
f(0.1) = 9(1/3)^0.1 ≈ 7.311
f(0.6) = 9(1/3)^0.6 ≈ 2.383
Estimated average rate of change = (2.383 - 7.311) / (0.6 - 0.1) = - 0.973
For the quadratic function, y = 9x^2 + (1/3)x, we have:
f(0.1) = 9(0.1)^2 + (1/3)(0.1) = 0.093
f(0.6) = 9(0.6)^2 + (1/3)(0.6) = 3.54
Estimated average rate of change = (3.54 - 0.093) / (0.6 - 0.1) = 7.894
Since the estimated average rate of change for the exponential function is negative (-0.973) and the estimated average rate of change for the quadratic function is positive (7.894), the exponential function has a negative estimated average rate of change over the interval [0.1,0.6].
Therefore, the correct answer is: the exponential function.