Answer:
Step-by-step explanation:
An exponential equation has the form
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The instantaneous rate of change of with respect to at the value is 18.
a) Geometrically speaking, the average rate of change of with respect to over the interval by definition of secant line:
(1)
Where:
, - Lower and upper bounds of the interval.
, - Function exaluated at lower and upper bounds of the interval.
If we know that , and , then the average rate of change of with respect to over the interval is:
The average rate of change of with respect to over the interval is 27.
b) The instantaneous rate of change can be determined by the following definition:
(2)
- Change rate.
, - Function evaluated at and .
If we know that and , then the instantaneous rate of change of with respect to is: