Answer:
a)
A(t) = 1,000,000 + 10,000,000t
B(t)= 0.01 +0.02t
b) No.
Step-by-step explanation:
a)<u> Penalty A:</u> 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
<u>Penalty B</u>: 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.