Aconstruction firm is trying to decide which of two models of a crane to purchase. model a costs $100,000 and requires $4,000 per year to maintain. model b has an initial cost of $78,000 and a maintenance cost of $13,000 per year. for how many years must model a be used before it becomes more economical than b? (round your answer to one decimal place.)

Let A and B be the functions which calculate the cost of purchase and maintenance of the models for x years.

The functions are as follows: 

A(x)=100,000+4,000x                                (dollars)

B(x)=78,000+13,000x                              (dollars)

Model A becomes more economical than Model B when A(x)<B(x), 

so we solve:

100,000+4,000x<78,000+13,000x  

100,000-78,000<13,000x-4,000x
 
         22,000< 9000x
               
                 22<9x

                    x>22/9=2.444

Model A becomes more economical in the third year, that is after the first 2 years.

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