The area A of a blot of ink is growing such t | vedclass

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(C) The area of the ink blot is given by the function $A(t) = 3t^2 + 7$.To find the rate of increase of the area,we need to calculate the derivative o

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$12$

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(C) The area of the ink blot is given by the function $A(t) = 3t^2 + 7$.To find the rate of increase of the area,we need to calculate the derivative of $A$ with respect to time $t$,which is $\frac{dA}{dt}$.Using the power rule for differentiation,$\frac{d}{dt}(3t^2 + 7) = 3(2t) + 0 = 6t$.Now,we evaluate this rate at $t = 2 \, s$:$\frac{dA}{dt} \Big|_{t=2} = 6(2) = 12 \, cm^2/s$.Thus,the rate of increase of the area at $t = 2 \, s$ is $12 \, cm^2/s$.

The area $A$ of a blot of ink is growing such that after $t$ seconds its area is given by $A = (3t^2 + 7) \, cm^2$. Calculate the rate of increase of area at $t = 2 \, s$. .......... $cm^2/s$

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