Power and Logarithmic Functions 4

Question

The area of a circular wave expands across a still pond such that its area is (2t)/(t+1) cm^2, t seconds after the wave begins. Write a formula for the circumference C of the circle as a function of t.

Answer 1

You have a formula for area as a function of t, and also you know that area = pi times radius squared

 

solve for r squared; then solve for r--it will be a function of t.  Then C = 2(pi)r

 

Details are left for you.

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

Area = πr²

 

C = 2πr

 

 

Since you are given the area, substitute the given expression into the formula for area to find the radius.

 

√(Area / π) = r

 

√[(2t) / (t - 1)π] = r

 

 

Now, we substitute this value of r into the formula for circumference.

 

C = 2π * √[(2t) / (t - 1)π]