that models Espeño A construction crew is lengthening a road. Let y represent th

Question

that models Espeño A construction crew is lengthening a road. Let y represent the total length of the road (in miles). Let x represent the number of days the crew has worked. Suppose that x and y are related by the equation 52 t3xy Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What was the road's length when the crew started working? miles What is the change per day in the road's length? miles

Explanation / Answer

when the crew started working, initially, at the beginning, the number of days they worked, was x = 0

hence, 52 + 3x = y gives at x=0 , has, y = 52

hence at the beginning, the road's length was, 52 miles

take x=n and x=n+1 be 2 consecutive days

at x=n , the length was, y(n) = 3n+52

and, at, x=n+1, y(n+1) = 3(n+1)+52

hence, the change in length per day increases by, y(n+1) - y(n) = 3(n+1)+52 - (3n+52) = 3 miles

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