A microorganism culture undergoes the following sequence of changes in one laboratory…

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems

Problem

A microorganism culture undergoes the following sequence of changes in one laboratory cycle: • The population first multiplies by a factor of

2^{5}

. • Then

2^{3}

bacteria are removed. (This step is represented algebraically by multiplying by

2^{-3}

.) • The remaining culture is then subjected to a process equivalent to squaring

2^{4}

times. • Finally,

2^{7}

bacteria are separated out of the culture. The combined effect can be represented by the expression

E_3 = 2^{5}\times2^{-3}\times(2^{4})^{2}\div2^{7}.

Answer the following questions. (i) Simplify

E_3

and express it in the form

2^{n}

. (ii) State the value of

n

. (iii) If the initial culture contained exactly one bacterium, how many bacteria are present after the entire laboratory cycle is completed?