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.

three shapes. three areas to find. three areas to add together to find the whole area. gotcha.

Step-by-step explanation:

smaller rectanglelarger rectangleright triangle smaller rectangle:

length is 7 cm and width is 4 cm, so the area is 28 square cm

larger rectangle:

width is 4 cm and length is 10 cm, so the area is 40 square cm

Because the weird shape's bottom length was 13 cm. There are 3 cm and 7 cm on the top length(s) of the weird shape, next to each other. Looking at the dash lines, when adding 3 cm and 7 cm together, the larger rectangle's length is 10 cm.

right triangle:

base is 3 cm and height is 8 cm, so the area is (3x8)/2 = 24/2 = 12 square cm

With knowledge from figuring out the larger rectangle's length being 10 cm and the weird shape's bottom length being 13 cm, we know the right triangle's base is 3 cm. (13 cm - 10 cm = 3 cm for the base of the right triangle).

Due to adding 4 cm and 4 cm of weird shape's width, which is also a right triangle's height.

weird shape's area from adding three shapes' areas:

28 + 40 + 12

= 80 square cm (ANSWER)