The area 'A' of a blot of ink is growing such that after 't' second.
`A=3t^(2)+(t)/(5)+7`
Calculate the rate of increase of area after five seconds.

Explanation

To solve the problem of calculating the rate of increase of the area 'A' of a blot of ink after 5 seconds, we will follow these steps:

### Step 1: Write down the given function for area A
The area of the inkblot is given by the function:
\[ A(t) = 3t^2 + \frac{t}{5} + 7 \]

### Step 2: Differentiate the function A with respect to time t
To find the rate of increase of area with respect to time, we need to differentiate A with respect to t:
\[ \frac{dA}{dt} = \frac{d}{dt}(3t^2) + \frac{d}{dt}\left(\frac{t}{5}\right) + \frac{d}{dt}(7) \]
Calculating each term:
- The derivative of \(3t^2\) is \(6t\).
- The derivative of \(\frac{t}{5}\) is \(\frac{1}{5}\).
- The derivative of a constant (7) is 0.

Thus, we have:
\[ \frac{dA}{dt} = 6t + \frac{1}{5} \]

### Step 3: Substitute t = 5 seconds into the derivative
Now, we need to find the rate of increase of area after 5 seconds. We substitute \(t = 5\) into the derivative:
\[ \frac{dA}{dt} \bigg|_{t=5} = 6(5) + \frac{1}{5} \]
Calculating this gives:
\[ \frac{dA}{dt} \bigg|_{t=5} = 30 + \frac{1}{5} \]
To add these, we can express 30 as a fraction:
\[ 30 = \frac{150}{5} \]
So,
\[ \frac{dA}{dt} \bigg|_{t=5} = \frac{150}{5} + \frac{1}{5} = \frac{151}{5} \]

### Step 4: Convert the result to decimal form
Now, we convert \(\frac{151}{5}\) to decimal:
\[ \frac{151}{5} = 30.2 \]

### Conclusion
The rate of increase of the area after 5 seconds is:
\[ \frac{dA}{dt} \bigg|_{t=5} = 30.2 \text{ square units per second} \]