A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate which the area within the circle is increasing after a) 1 second, b) 3 seconds, and c) 5 seconds.
What can you conclude?

a)

b)

c)

We can conclude that the area of the circle increases faster when the time increases.

Step-by-step explanation:

First let's write the equation for the area of the circle:

The rate that the radius of the circle increases is 60 cm/s, so we have:

To find the rate that the area increases, let's take the derivative of the equation of the area in relation to time:

a)

Using t = 1, we have:

b)

Using t = 3, we have:

c)

Using t = 5, we have:

We can conclude that the area of the circle increases faster when the time increases.

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).