# Given the demand function `p=S(x)=10(e^(0.02x) - 1)` , find the average price (in dollars) over the supply interval [20, 30].

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### 1 Answer

The demand function is `p = S(x) = 10*(e^(0.02*x) - 1)`

In the interval [20, 30], the sum of the price for all the values of x is given by:

`int_(20)^30 10*(e^(0.02*x) - 1) dx`

=> `((10*e^(0.02x))/0.02 - 10x)_(20)^30`

=> `(500*e^(0.02x)) - 10x)_(20)^30`

=> `500*e^(0.02*30) - 300 - 500*e^(0.02*20) + 200`

`~~65.14`

**The average price is $65.14**