Question

Barry’s Bagel Emporium sells a dozen bagels for $5.00. This price is no longer high enough to create a profit. The owner decides to raise the price. He does not want to alarm his customers with too large of an increase. He is considering four different plans.

Plan A: Raise the price by $0.05 each week until the price reaches $8.00.

Plan B: Raise the price by 10 percent each week until the price reaches $8.00.

Plan C: Raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00.

Plan D: Raise the price by $0.25 each week until the price reaches $8.00.

Which plan will result in the price of the bagels reaching $8.00 fastest?
plan A
plan B
plan C
plan D

Answer 1

Plan B.

Calculations:
- A: $0.05/week ⇒ 3.00/0.05 = 60 weeks.
- B: multiply by 1.10 each week, solve 5(1.1)^n ≥ 8 ⇒ (1.1)^n ≥ 1.6 ⇒ n = ln(1.6)/ln(1.1) ≈ 4.93 ⇒ reaches $8 on the 5th week.
- C: given as 6 weeks.
- D: $0.25/week ⇒ 3.00/0.25 = 12 weeks.

So plan B is fastest.