A rain drop hitting a lake makes a circular ripple. Suppose the radius, in inches, grows as a function of time in minutes according to r(t)=26t+1−−−−√, and answer the following questions. Find a function, A(t), for the area of the ripple as a function of time.

A(t) = 676π(t+1)

Correct question:

A rain drop hitting a lake makes a circular ripple. Suppose the radius, in inches, grows as a function of time in minutes according to r(t)=26√(t+1), and answer the following questions. Find a function, A(t), for the area of the ripple as a function of time.

Step-by-step explanation:

The area of a circle is expressed as;

A = πr^2

Where, A = Area

r = radius

From the case above.

The radius of the ripple is a function of time

r = r(t) = 26√(t+1)

So,

A(t) = π[r(t)]^2

Substituting r(t),

A(t) = π(26√(t+1))^2

A(t) = π(676(t+1))

A(t) = 676π(t+1)