Derek owns a landscape business. he charges a fixed fee of $30 plus $1 per 1,000 square feet of lawn mowed. derek's earnings (in dollars) in the past five weeks are {204, 344, 450, 482, 504}. to find the corresponding square footage of lawn mowed, construct a function that models the total area of lawn that derek mows based on his earnings.

From the given problem statement alone, we can say that the equation relating the area of the lawn mowed and the earnings has a linear relationship. That is because there is a constant increase in the earnings per area which is $1 per 1000 square feet.

Therefore the equation must be in the form of:

y = m x + b

where,

y = is the total earnings

m = is the fee per area = 1 / 1000

x = is the area of the lawn

b = is the fixed fee = 30

Therefore the equation becomes:

y = 0.001 x + 30

Rewriting this in terms for x since we are to find the area:

x = (y – 30) 1000

when y = 204

x = (204 – 30) 1000 = 174,000 square feet

when y = 344

x = (344 – 30) 1000 = 314,000 square feet

when y = 450

x = (450 – 30) 1000 = 420,000 square feet

when y = 482

x = (482 – 30) 1000 = 452,000 square feet

when y = 504

x = (504 – 30) 1000 = 474,000 square feet