An angler hooks a trout and begins turning her circular reel at 1.5 rev/s. Assume the radius of the reel (and the fishing line on it) is 2 inches.
a. Let R equal the number of revolutions the angler has turned her reel and suppose L is the amount of line that she has reeled in. Find an equation for L as a function of R.

Verified step by step guidance

1. Identify the relationship between the number of revolutions R and the length of the fishing line L that is reeled in. Each complete revolution of the reel corresponds to a certain length of line being pulled in.
2. Calculate the circumference of the reel using the formula for the circumference of a circle, which is C = 2πr, where r is the radius of the reel. Here, r = 2 inches.
3. Express the length of the line L in terms of the number of revolutions R. Since each revolution reels in a length equal to the circumference, we can write L = C * R.
4. Substitute the expression for the circumference from step 2 into the equation from step 3 to get L as a function of R: L = (2π * 2) * R.
5. Simplify the equation to express L in a more compact form, resulting in L = 4πR, which shows the direct relationship between the length of the line and the number of revolutions.