Question

The area of a blot of ink is growing such that after t seconds its area is given by A=(3t square +7) cm square. Calculate the rate of increase of area at t=5 second.


full steps required

Answer 1

Aloha !!!


Thank you for asking Such a Tricky + Interesting question 

The main concept which we use over here is to Differentiate this isn't it ? 

and we know differentiation is nothing but to split the number and is mainly used for the slope related question 

• Given that 

A = 3t²+ 7 

Here we can find out the value of A easily if we differentiate it , 

On doing differentiation we obtain

area = dx/dt

= d ( 3t² + 7 ) / dt = 6t

we are given that t = 5
second 

Now putting t = 5 


A = 6 × 5 

A = 30 cm²

Hope this helps you ☺

Answer 2

[0010001111]... Hello Locomaniac... [1001010101]
Here's your answer...

Its kinda awkward answering after a person has already answered, that too pretty awesomely, but still...
Let the area of the blot at time t be a. Then the rate of increase in the blot's area will be a/t.
Since we want the rate of increase at a specific time, we need the instantaneous rate of increase, which can be found using differentiation.
$a = 3 {t}^{2} + 7 \\ \frac{da}{dt} = 3 \times 2 {t}^{2 - 1} + 7 \times 0 {t}^{0 - 1} \\ = 6t$
Now we put t's value given in the question, in this equation.
So...
$\frac{da}{dt} = 6 \times 5 = 30 \: {cm}^{2} \: per \: s$
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