1) Look at the growing pattern below. How many squares will it take to make the nth figure in this pattern?
2) What if we made a pattern by joining pentagons? If the length of each side of the pentagon is 3 units, then what would be the perimeter of nth pentagons joined together? Note: The perimeter is the distance around the outside of the figure.
3) Variations of this problem have appeared in many places. Jack and Jill decide to start a rumor that there will be no school on the following Monday. What if each person tells exactly 2 people? How long will it take now? Assume that the rate for telling the next 2 people is 1 hour. That is, initially Jack and Jill know; after 1 hour, 2 more people know; after 2 hours, 4 more people know, . . . .
4) Consider the following table of numbers.
(a) Describe the pattern in your own words.
(b) Find the value of y when x is 100.
(c) Find a general expression for finding the nth term in your own words.
(d) Translate part (c) into function notation. f(x) =