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A simple stand – alone software utility is to be developed in ‘C’ programming by a team of software experts for a computer running Linux and the overall size of this software is estimated to be $20,000$ lines of code. Considering $(a,b)=2.4,1.05)$ as multiplicative and exponention factor for the basic COCOMO effort estimation equation and $(c,d)=(2.5, 0.38)$ as multiplicative and exponention factor for the basic COCOMO development time estimation equation, approximately how long does the software project take to complete?

1. $10.52$ months
2. $11.52$ months
3. $12.52$ months
4. $14.52$ months

Basic COCOMO Model

The basic COCOMO model gives an approximate estimate of the project parameters. The basic COCOMO estimation model is given by the following expressions:

$20,000 LOC = 20 KLOC$

$Effort = a * {(KLOC)}^b$PM

$T_{dev} = c * {(Effort)}^d$Months

$Effort = 2.4 * {(20)}^{1.05} PM$

$= 55.756$

$T_{dev} = 2.5 * {(55.756)}^{0.38} Months$

$= 11.52$ Months

means use of binomial expansion
maybe, I never used binomial expansion for such questions.
then how u can do approximation here  like 20 raised to power 1.05  or 55.756 raised to power .38

20,000 LOC (Lines of Code) = 20K LOC (Given)

(a,b) = (2.4, 1.05)       (Given)

(c,d) = (2.5,0.38)        (Given)

The basic COCOMO model gives an approximate estimate of the project parameters. The basic COCOMO estimation model is given by the following expression:

Effort = a * (KLOC)b PM         (PM = Person Months)

T dev = c * (Effort)d months     (T dev = Development TIme )

Effort = 2.4 * (20)1.05 PM

= 2.4 * 23.231 = 55.756 PM

T dev = 2.5 * (55.756)0.38 months

= 2.5 * 4.608 = 11.52 months

Therefore, time taken for completion of the software project  is 11.52 months

Thanks roma_nagpal but my question is how to solve exponential part as calculator is not allowed in NET exam.
Well there is not an easy way for this but may be binomial expansion theorem and some log tables could help a little bit

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