Question

1. Ordering a pizza with a group of friends often leads to a heated argument! With so many toppings available the number of possible pizzas is countless - or is it?

   # of Available Toppings	# of Different Pizzas
   0	1
   1	2
   2
   3
   4
   5
   6
   7
   8

   1. Complete the following table showing the relationship between the number of toppings available for a pizza, and the total number of possible pizzas. Remember, you may choose to use none, some, or all of the available toppings. Be sure to justify each answer. This first couple of entries are done for you.
   2. Graph the data from your table.
   3. What type of function is represented by the data above? Justify your answer

Answer 1

Question 1

Here is the completed table.

As for each pizza choices we may choose to use none, some or all availble toppings.

so here possible type of pizzas when there are n toppings are

= No toppings + 1 topping + 2 topping + 3 topping

= ⁿC₀ + ⁿC₁ + ⁿC₂ + ⁿC₃ + ...ⁿC_n  =2ⁿ

# of Available Toppings	# of Different Pizzas
0	1
1	2
2	4
3	8
4	16
5	32
6	64
7	128
8	256

(c) Here 2ⁿ is exponetial function. We can justify it by graph here.