Acarton of milk has spilled on a tile floor. the milk flow can be expressed with the function m(t) = 9t, where t represents time in minutes and m represents how far the milk is spreading.

the flowing milk is creating a circular pattern on the tile. the area of the pattern can be expressed as a(m) = πm2.

part a: find the area of the circle of spilled milk as a function of time, or a[m(t)]. show your work. (6 points)

part b: how large is the area of spilled milk after 2 minutes? you may use 3.14 to approximate π in this problem. (4 points)

1. d.90

2. e. none of these (80)

3. a. 0

4. b. 6

5. e. none of these (10)

6. a. 5

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for