Compare the estimated average rate of change of an exponential function and a quadr...
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Problem
Compare the estimated average rate of change of an exponential function and a quadratic function over an interval. Determine which function has a negative estimated average rate of change.
Step-by-step solution
Calculate the average rate of change for both functions over the interval [0.1, 0.6]. For $y = 9(\frac{1}{3})^x$, the average rate of change is approximately -12.9. For $y = 9x^2 + \frac{1}{3}x$, the average rate of change is approximately 3.15. Thus, the exponential function has a negative average rate of change.
Answer
the exponential function