felixs feed mill sells chicken feed for $8.00 per bag. this price is no longer high enough to create a…

felixs feed mill sells chicken feed for $8.00 per bag. this price is no longer high enough to create a profit. felix decides to raise the price. he is considering four different plans.\n\nplan a: raise the price by $0.10 each week until the price reaches $12.00.\n\nplan b: raise the price by 10 percent each week until the price reaches $12.00.\n\nplan c: raise the price by the same amount each week for 8 weeks, so that in the eighth week the price is $12.00.\n\nplan d: raise the price by $0.25 each week until the price reaches $12.00.\n\nwhich plan will result in the price of the feed reaching $12.00 fastest?\n\n○ plan a\n○ plan b\n○ plan c\n○ plan d

felixs feed mill sells chicken feed for $8.00 per bag. this price is no longer high enough to create a profit. felix decides to raise the price. he is considering four different plans.\n\nplan a: raise the price by $0.10 each week until the price reaches $12.00.\n\nplan b: raise the price by 10 percent each week until the price reaches $12.00.\n\nplan c: raise the price by the same amount each week for 8 weeks, so that in the eighth week the price is $12.00.\n\nplan d: raise the price by $0.25 each week until the price reaches $12.00.\n\nwhich plan will result in the price of the feed reaching $12.00 fastest?\n\n○ plan a\n○ plan b\n○ plan c\n○ plan d

Answer

Explanation:

Step1: Calculate weeks for Plan A

Find the price increase amount: $12 - 8=4$. Divide by the weekly increase: $\frac{4}{0.1}=40$ weeks.

Step2: Calculate weeks for Plan B

Let $n$ be the number of weeks. The formula is $8\times(1 + 0.1)^n=12$. Then $(1.1)^n=\frac{12}{8}=1.5$. Taking the natural - logarithm of both sides, $n\ln(1.1)=\ln(1.5)$. So $n=\frac{\ln(1.5)}{\ln(1.1)}\approx\frac{0.4055}{0.0953}\approx4.26$ weeks.

Step3: Calculate weeks for Plan C

The price needs to increase by $12 - 8 = 4$ in 8 weeks. But we want to know when it reaches $12$. Since it reaches $12$ in 8 weeks.

Step4: Calculate weeks for Plan D

Find the price increase amount: $12 - 8 = 4$. Divide by the weekly increase: $\frac{4}{0.25}=16$ weeks.

Answer:

B. plan B