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.¹

Suppose the city of Yonkers is offered two alternative fines by the judge.

PenA:1 million dollars on August 2 and the fine increases by 10 million dollars each day thereafter.

PenB:1 cent on August 2 and the fine doubles each day thereafter.

(a)Iftrepresents the number of days after August 2, express the fine incurred as a function of t under

Penalty A:

A(t)= 1000000 + 10000000*t dollars

Penalty B:

B(t)= 0.01(2)^t dollars

(b)Assuming your formulas in part(a)hold for t0, is there a time such that the fines incurred under both penalties are equal?

Round your answer to the nearest integer. If there is no such time, enter NA.

Both penalties are equal after _________ days.