At a farm, four employees harvest 48 pounds of food over a certain number of hours. Each employee works the number of hours shown. Employee works six hours, employee B works four hours, employee seat work six hours, and employee D works eight hours. The number of pounds of food harvested by each employee is proportional to the number of hours worked. Fill in the table with the amount of food, in pounds, each employee harvested.

1. 1024 functions

2. 59049 functions

3. 1048576 functions

4. 9765625 functions

Step-by-step explanation:

Denote two events with A and B, product rule states that if event A can occur in x number of ways and event B can occur in y number of ways, the two events (A and B) can occur in sequence in

x * y ways

i.e. xy ways

If a set has a range of n elements, there are n possible ways in each element

First element: n ways

Second element: n ways

Third element: n ways

Fourth elements; n ways

Fifth element: n ways

Sixth element: n ways

Seventh element: n ways

Eight elements; n ways

Ninth element: n ways

Tenth element: n ways

As stated above in the product rule, we have n*n*n*n*n*n*n*n*n*n*n = n^10

a. n = 2 elements

Number of Possible Functions = 2^10 = 1,024 functions

b. n = 3 elements

Number of Possible Functions = 3^10 = 59,049 functions

c. n = 4 elements

Number of Possible Functions = 4^10 = 1,048,576 functions

d. n = 5 elements

Number of Possible Functions = 5^10 = 9,765,625 functions