To express: The radius of the balloon as a function of time t.
The function of the radius of the balloon in terms of time t is .
It is given that the balloon is being inflated and therefore the radius is increasing at a rate of 2 cm/s.
Let the radius of the balloon be r.
Recall the formula, Distance = Time × Speed.
Note that the distance is same as radius.
Substitute t for time and 2 for speed in a distance formula.
Thus, the function is where r(t) is measured in cm.
Therefore, the radius of the spherical balloon after t seconds is .
To find: The expression for and interpret where V is the volume of the function of radius.
The value of , which represents the area of the circular ripple at a time t.
Area of the circle is, (1)
The composite function is defined as .
From part (a), the value of .
Substitute in equation (1),
Thus, , which represents the area of the circular ripple with respect to the radius of time t.
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