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A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are related by s=60000−310000e−0.0007x. 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.
This is what I did so far:
s = weekly sales
x = weekly advertising
x = 2000
S’ = (0 + 310000(-0.0007e^(-0.0007x))
S’ = -217e^(-0.0007x)
S'(2300) = -217e(-0.0007(2300))
S'(2300) = -43.38
x as x(t), so S = S(x(t)). So when you take the derivative of e-0.0007x, it’s -0.0007e-0.0007x(dx/dt). Then, after simplifying, you plug in dx/dt = 300