Question

Amoeba is a unicellular organism that has the ability to alter its shape. It carries out binary fission to increase its number, that is, splits into two halves. In a certain colony, at the initial stage, there are 18 amoebae. Find the number of amoebae in the colony after the 6th fission in the form of (2^m times 3^n) where (m) and (n) are positive integers.

a) (2^6 times 3^5)
b) (2^5 times 3^6)
c) (2^4 times 3^7)
d) (2^7 times 3^4)

Answer 1

The number of amoebae in the colony after the 6th fission is (2^7 * 3^4), which corresponds to option d) in the given choices.

Step-by-step explanation:

Binary fission is the process by which amoeba reproduces asexually, splitting into two halves. In the initial stage of the colony, there are 18 amoebae. After the 6th fission, we can calculate the number of amoebae using the formula: 18 * (2^6). This gives us 1152 amoebae. However, we need to express the answer in the form of (2^m * 3^n). In this case, 1152 can be written as 2^7 * 3^4. Therefore, the number of amoebae in the colony after the 6th fission is (2^7 * 3^4), which corresponds to option d) in the given choices.