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the length of the sides of a square are initially 0 cm and increase at a constant rate of 7 cm per second. suppose the function f determines the area of the square (in cm2) given a number of seconds, t , since the square started growing. write a function formula for f .

Answer :

The function of the area of the square is A(t) = 49t².

A function is a relation between the input abd output values.

The length of a square's side starts from 0 cm and increases at a constant rate of 7 cm per second.

Let us assume that the function 'f' determines the area of the square (in cm²)

Also Lets  the length of side of square is x

rate of change of length with respect to time can be denoted as (dx/dt) = 7 cm/sec

⇒ x = 7*t

Area of square = ( length of side )²

{as the length of side is 7t} {varies by time}

Area of square A(t) = ( 7*t )²

Therefore, The function of the area of the square is A(t) = 49t².

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