Doubling Numbers #12

Question

Dr. Albert A. Bartlet (University of Colorado) developed the following analogy: Suppose you have a glass jar in which a single bacterium is placed at 12:00 pm. Suppose that at 12:01 pm the bacterium divides into two bacteria; at 12:02 each of these bacteria divide into two, making a total of four bacteria; at 12:03 each of these bacteria divide into two, making a total of eight bacteria; and so on, until 1:00 pm when the bacteria colony runs out of space in the jar and dies as a consequence. How many bacteria are in the jar at 12:16 pm? Do not put commas in your answer.

Answer 1

a_n=a₀rⁿ

a₀=1

a₁=2

a₁₆=2¹⁶=65536

Answer 2

This is a geometric sequence.

 

a_n = a₁r^n-1, where a_n = nth term, a₁ = first terms, r = common ratio

 

a₁₆ = 1 (2)¹⁵

a₁₆ = 32768

 

The jar contains 32768 bacteria.