Final answer:
Michael's earnings for mowing lawns are calculated by the function f(x) = 25x, which means for each lawn mowed he earns $25, and this is multiplied by the total number of lawns mowed.
Step-by-step explanation:
The function rule that Michael would use to calculate his earnings for mowing lawns, given that he charges $25 for each lawn, is a direct function of the number of lawns mowed. In mathematical terms, where f(x) represents Michael's earnings and x is the number of lawns mowed, the correct function is f(x) = 25x.
This choice is representative of a straightforward linear relationship between Michael's earnings and the number of lawns: for every additional lawn he mows, he earns another $25. Thus, the function is a simple multiplication of the number of lawns by the fixed per-lawn rate with no additional fees or subtracted amounts.
The other options do not correctly represent the situation:
- B) f(x) = 25 + x suggests a constant fee plus an amount that depends on the number of lawns, which is not the case.
- C) f(x) = x/25 incorrectly implies that each lawn mowed contributes to only 1/25 of the total earnings, which would not give the correct total amount.
- D) f(x) = 25 - x incorrectly suggests a decreasing function where earnings reduce with each additional lawn, which is contrary to the given situation.
Therefore, the correct calculation for Michael's earnings based on the number of lawns mowed is represented by option A) f(x) = 25x.