barrys bagel emporium sells a dozen bagels for $5.00. this price is no longer high enough to create a…

barrys 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

barrys 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

Explanation:

Step1: Calculate weeks for Plan A

Find the price - increase amount: $8 - 5=3$. Divide by the weekly increase: $\frac{3}{0.05}=60$ weeks.

Step2: Calculate weeks for Plan B

Let $n$ be the number of weeks. The price formula is $P = 5\times(1 + 0.1)^n$. We need to solve $5\times(1.1)^n=8$. So, $(1.1)^n=\frac{8}{5} = 1.6$. Taking the natural - logarithm of both sides: $n=\frac{\ln(1.6)}{\ln(1.1)}\approx \frac{0.4700036292}{0.0953101798}\approx 4.93$ weeks.

Step3: Calculate weeks for Plan C

The price increases over 6 weeks from $5$ to $8$.

Step4: Calculate weeks for Plan D

Find the price - increase amount: $8 - 5 = 3$. Divide by the weekly increase: $\frac{3}{0.25}=12$ weeks.

Answer:

B. plan B