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ight) - 10 = 2(5 - \sqrt{7}) - 10 = -2\sqrt{7} < 0 \quad ( ext{local maximum}).

Thus, the revenue growth rate is maximized at \( t = rac{5 - \sqrt{7}}{9} \).

oxed{rac{5 - \sqrt{7}}{9}}

A pharmacologist is studying the concentration of a new Alzheimer's drug in the bloodstream, modeled by the function \( C(x) = 5x^2e^{-x} \). Determine the dosage level \( x \) that maximizes the concentration.

To find the dosage level that maximizes the concentration, we first find the derivative of \( C(x) \):

C'(x) = rac{d}{dx}(5x^2e^{-x}).

Using the product rule, where \( u = 5x^2 \) and \( v = e^{-x} \), we have:

C'(x) = u'v + uv' = (10x)e^{-x} + 5x^2(-e^{-x}) = e^{-x}(10x - 5x^2).

Set \( C'(x) = 0 \) to find critical points:

e^{-x}(10x - 5x^2) = 0.

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