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 under
penalty a:
a(t)= dollars
penalty 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?

a)

A(t) = 1,000,000 + 10,000,000t

B(t)= 0.01 +0.02t

b) 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 + 10,000,000t

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

A(t) = 0.01 + 2t(0.01) = 0.01 + 0.02t

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?

To solve this, we would have to equal both formulas and solve for t.

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.

a and c

step-by-step explanation: