1. When oil was spilled out in the middle of a lake, it spread out on the surface of the water in a circular pattern. The radius of the circular pattern increased at a rate of 4 feet per minute. ((() = 4tft/min)

A. [3 pts) How fast was the area of the circular pattern increasing per minute? Construct the composite function to show how the area was increasing each minute. ( A() = ft/min).

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facundo3141592 facundo3141592 · Answer 1 · 2022-04-13T12:07:05+02:00

The rate of change of the area as a function of time is:

A'(t) = 6.28*(R₀ + 4ft/min*t)*(4ft/min)

Remember that for a circle of radius R, the area is:

A = 3.14*R^2

Now, if the radius increases at a rate of 4 ft/min, then we can rewrite R as:

R(t) = R₀ + 4ft/min*t

Where t is the time in minutes, and R₀ is the initial radius.

So the area function is:

A(t) = 3.14*(R₀ + 4ft/min*t)^2

The rate of change is given by the differentiation with respect to t, it is:

A'(t) = 2*3.14*(R₀ + 4ft/min*t)*(4ft/min)

A'(t) = 6.28*(R₀ + 4ft/min*t)*(4ft/min)

The rate at which the area increases, as a function of time, is given by:

A'(t) = 6.28*(R₀ + 4ft/min*t)*(4ft/min)

If you want to learn more about rates of change, you can read:

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