Mathematics

Question

First six shipments:
10, 16, 22, 28, 34, 40
A factory is producing a linear number of objects in each shipment. If x = the shipment number, which function can be used to determine how many objects are in that shipment?

1 Answer

  • For problems like this, we need to find the pattern between the set of numbers to create a general equation for f(x). Given that x is the shipment number, let us first observe the first six shipments' behavior.
    1  10 |
    2  16 = 10 + 1(6) |
    3  22 = 10 + 2(6) |
    4  28 = 10 + 3(6)|  
    5  34 = 10 + 4(6) |
    6  40 = 10 + 5(6) |

    From these, we can observe that given x number of shipments, the total number of objects would be [tex] 10 + (x-1)6 = 10 + 6x - 6 = 6x +4 [/tex]. Thus, given f(x), we have 

    [tex] f(x) = 6x + 4 [/tex]
    Answer: f(x) = 6x + 4

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