Final answer:
To calculate the summer earnings from mowing lawns, create a table multiplied by $18 per lawn and five lawns per day for daily earnings. Use an explicit equation E = 90d and a recursive equation En = En-1 + 90 for total earnings. Working 60 days earns $5400, with domain and range as sets of positive integers and multiples of $90, respectively.
Step-by-step explanation:
The scenario described involves calculating earnings over a period as a result of mowing lawns. First, to make a table that shows the earnings for each day you would work, you would multiply the number of lawns mowed per day by the payment per lawn. Since the payment is $18 per lawn and you can mow five lawns per day, your daily earnings would be $18 × 5 = $90.
To write an explicit equation to model the total earnings (E) after d days, you would use E = 90d. This simply states that your total earnings are $90 times the number of days you work.
The recursive equation would be based on the idea that each day's total earnings are the previous day's total plus $90. If En is the total earnings after n days, then the recursive equation would be En = En-1 + 90, with E1 = 90 as the base case.
To calculate your earnings if you worked 60 days over the summer, you'd use the explicit equation: $90 × 60 = $5400.
The domain of this function would be the set of all possible workdays, which we'll assume to be positive integers (since you can't work a fraction of a day in this context). The range would be all possible total earnings, which are multiples of $90.