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.\n\nplan a: raise the price by $0.05 each week until the price reaches $8.00.\n\nplan b: raise the price by 10 percent each week until the price reaches $8.00.\n\nplan c: raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00.\n\nplan d: raise the price by $0.25 each week until the price reaches $8.00.\n\nwhich plan will result in the price of the bagels reaching $8.00 fastest?\n\n○ plan a\n○ plan b\n○ plan c\n○ 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.\n\nplan a: raise the price by $0.05 each week until the price reaches $8.00.\n\nplan b: raise the price by 10 percent each week until the price reaches $8.00.\n\nplan c: raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00.\n\nplan d: raise the price by $0.25 each week until the price reaches $8.00.\n\nwhich plan will result in the price of the bagels reaching $8.00 fastest?\n\n○ plan a\n○ plan b\n○ plan c\n○ plan d

Answer

Explanation:

Step1: Calculer le nombre de semaines pour le Plan A

Le prix initial est de 5 dollars et on veut arriver à 8 dollars. L'augmentation par semaine est de 0,05 dollars. On utilise la formule $n=\frac{8 - 5}{0.05}$. $n=\frac{3}{0.05}=60$ semaines.

Step2: Calculer le nombre de semaines pour le Plan B

On utilise la formule de la progression géométrique $P = P_0(1 + r)^n$, où $P_0 = 5$, $r=0.1$ et $P = 8$. On doit résoudre l'équation $8 = 5(1 + 0.1)^n$ pour $n$. $\frac{8}{5}=(1.1)^n$, $1.6=(1.1)^n$. En utilisant le logarithme, $n=\frac{\ln(1.6)}{\ln(1.1)}\approx 4.93$ semaines.

Step3: Calculer le nombre de semaines pour le Plan C

Le prix doit passer de 5 dollars à 8 dollars en 6 semaines. On suppose une augmentation constante par semaine. Soit $x$ l'augmentation par semaine. On a $5+6x = 8$, $6x=8 - 5=3$, $x = 0.5$ dollars par semaine. Le prix atteint 8 dollars en 6 semaines.

Step4: Calculer le nombre de semaines pour le Plan D

Le prix initial est 5 dollars et on veut arriver à 8 dollars avec une augmentation de 0.25 dollars par semaine. On utilise la formule $n=\frac{8 - 5}{0.25}$. $n=\frac{3}{0.25}=12$ semaines.

Answer:

B. plan B