Aretail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are related by s equals 40 comma 000 minus 30 comma 000 e superscript negative 0.0004 xs=40,000−30,000e−0.0004x. the current weekly advertising costs are$2 comma 5002,500, and these costs are increasing at a rate of$400400 per week. find the current rate of change of sales. the current rate of change of sales is $nothing per week. (round to the nearest dollar as needed.)

The current rate of change of sales is $4 per week.

Step-by-step explanation:

Let as consider the weekly sales function

where, s represents the weekly sales and x is the weekly advertising costs (both in dollars).

Differentiate with respect to x.

            .... (1)

Here, represents the rate of change of sales at weekly advertising costs x.

Current weekly advertising costs = $2500

Substitute x=2500 in equation (1).

Therefore, the current rate of change of sales is $4 per week.

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step-by-step explanation: