To compare the estimated average rate of change of the exponential function
The average rate of change of a function
For the exponential function
-
Evaluate at
: -
Evaluate at
: -
Calculate average rate of change:
The average rate of change for the exponential function over
For the quadratic function
-
Evaluate at
: -
Evaluate at
: -
Calculate average rate of change:
The average rate of change for the quadratic function over
Summary of Results:
- Average rate of change of the exponential function over
: approximately (positive). - Average rate of change of the quadratic function over
: (positive).
Conclusion:
Both functions have a positive estimated average rate of change over the interval
neither function.