Ithink it's 50 now a barrel of tomato sauce has spilled on a tile floor. the sauce flow can be expressed with the function r(t) = 2t, where t represents time in minutes and r represents how far the sauce is spreading. the spilled sauce is creating a circular pattern on the tile. the area of the pattern can be expressed as a(r) = πr2. part a: find the area of the circle of spilled sauce as a function of time, or a[r(t)]. show your work. (6 points) part b: how large is the area of spilled sauce after 5 minutes? you may use 3.14 to approximate π in this problem. (4 points)

Here barrel of tomato sauce has spilled on a tile floor.

The function represents how the sauce is flowing, where, 't' represents time in minutes, and 'r' represents how far the sauce is spreading.

The spilled sauce is creating a circular pattern on the tile and the area of pattern is expressed as

A. Now we have to find the area of circle of spilled sauce as a function of time:

.

Now, we know that

and

plugging the value of 'r' as function of time in the area of the pattern, we get:

So the area of the circular pattern as a function of time is given as:

B. We have to find how large is the area of spilled sauce after 5 minutes.

plugging the value of 't' in the equation of the area as a function of time,

we get:

(we have taken )

Therefore, square units

both equations and proportions are better.