a) You need to remember that the average rate of change is the change in y value over the change in x value for two distinct points, hence if x changes from 10 to 101, then you may evaluate the average rate of change of `C(x)` such that:

`(C(101) - C(100))/(101 - 100)`

You need to evaluate `C(101)` such that:

`C(101) = 8000 + 0.15*101^2 = 9530.15`

You need to evaluate `C(100)` such that:

`C(100) = 8000 + 0.15*100^2 = 9500`

`(C(101) - C(100))/(101 - 100) = (9530.15 - 9500)/1`

`(C(101) - C(100))/(101 - 100) = 30.15`

**Hence, evaluating the average rate of change of C(x) considering
the given changes yields `(C(101) - C(100))/(101 - 100) =
30.15.`**

b) You need to find the instantaneous rate of change, hence, you need to differentiate the function C(x) with respect to x such that:

`C'(x) = 0.3x`

You need to evaluate C'(x) at x = 100 such that:

`C'(100) = 0.3*100 = 30`

**Hence, evaluating the instantaneous rate of change at `x =
100` yields `C'(100) = 30.`**

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