The area of dot of ink in `cm^(2)` is growing such that after 5s , `A = 3t^(2) +(t//5) +7` .Calculate the rate of increase of area after 5s.

Explanation

To solve the problem, we need to find the rate of increase of the area \( A \) of the dot of ink after 5 seconds. The area is given by the function:

\[ A(t) = 3t^2 + \frac{t}{5} + 7 \]

### Step 1: Differentiate the Area Function
We need to find the derivative of \( A(t) \) with respect to time \( t \) to determine the rate of increase of the area. The derivative \( \frac{dA}{dt} \) is calculated as follows:
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