On August 2nd, 1988, a US District Court judge imposed a fine on the city of Yonkers, New York, for defying a federal court order involving housing desegregation.Suppose the city of Yonkers is offered two alternative fines by the judge.(i) Penalty A: 1 million dollars on August 2 and the fine increases by 10 million dollars each day thereafter.(ii) Penalty B: 1 cent on August 2 and the fine doubles each day thereafter.(a) If t represents the number of days after August 2, express the fine incurred as a function of t underPenalty A:A(t)= __________ dollarsPenalty B:B(t)= __________ dollars(b) Assuming your formulas in part (a) hold for t≥0, is there a time such that the fines incurred under both penalties are equal?

Answer:a) A(t) = 1,000,000 + 10,000,000tB(t)= 0.01 +0.02tb) No.Step-by-step explanation:a) Penalty A: 1 million dollars on August 2 and the fine increases by 10 million dollars each day thereafter.If t represents the number of days after August 2,A(t) = 1,000,000 + 10,000,000tPenalty B: 1 cent on August 2 and the fine doubles each day thereafter.A(t) = 0.01 + 2t(0.01) = 0.01 + 0.02tb) Assuming your formulas in part (a) hold for t≥0, is there a time such that the fines incurred under both penalties are equal?To solve this, we would have to equal both formulas and solve for t.[tex]1,000,000 + 10,000,000t=0.01+0.02t\\9,999,999.98t=-999,999.99[/tex]By taking a look at this equation, we see that when we solve for t, t will be a negative number. Since the formulas are valid for t≥0, we can conclude that there won't be a time such that the fines are equal.