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Question

When the growth of a spherical cell depends on the flow of nutrients through the surface, it is reasonable to assume that the growth rate, $d V / d t$, is proportional to the surface area, S. Assume that for a particular cell $d V / d t=\dfrac{1}{3} \cdot S$. At what rate is its radius $r$ increasing?

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1 of 4In this exercise, let us find the rate at which the radius $r$ of a spherical cell is increasing. Given that the growth of the spherical cell depends on the transfer of nutrients through its surface. We assume that the growth rate, $dV/dt$ is proportional to the surface area such that: $dV/dt = \frac{1}{3}\cdot S$.

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