Math  /  Calculus

QuestionA retail store estimates that weekly sales ss and weekly advertising costs xx (both in dollars) are related by s=60000430000e0.0005xs=60000-430000 e^{-0.0005 x}
The current weekly advertising costs are 2000 dollars and these costs are increasing at the rate of 300 dollars per week. Find the current rate of change of sales. Rate of change of sales == \square

Studdy Solution
Calculate the rate of change of sales:
dsdt=2150.36787930023700.59\frac{ds}{dt} = 215 \cdot 0.367879 \cdot 300 \approx 23700.59
The current rate of change of sales is approximately:
23700.59\boxed{23700.59}

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