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\no plan a\no plan b\no plan c\no 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\no plan a\no plan b\no plan c\no plan d

Answer

Explanation:

Step1: Calculate weeks for Plan A

Find the price increase amount: $12 - 8=4$. Divide by increase per week. Let $n_A$ be the number of weeks. $n_A=\frac{12 - 8}{0.1}=\frac{4}{0.1}=40$.

Step2: Calculate weeks for Plan B

The price after $n$ weeks is $P = 8\times(1 + 0.1)^n$. We need to solve $8\times(1.1)^n=12$ for $n$. So, $(1.1)^n=\frac{12}{8} = 1.5$. Taking the natural - logarithm of both sides: $n\ln(1.1)=\ln(1.5)$. Then $n_B=\frac{\ln(1.5)}{\ln(1.1)}\approx\frac{0.4055}{0.0953}\approx4.26$.

Step3: Calculate weeks for Plan C

Let the amount of increase per week be $x$. We know that $8+8x = 12$. Solving for $x$ gives $8x=12 - 8 = 4$, so $x = 0.5$. And it takes 8 weeks as given in the plan.

Step4: Calculate weeks for Plan D

Let $n_D$ be the number of weeks. $n_D=\frac{12 - 8}{0.25}=\frac{4}{0.25}=16$.

Answer:

B. plan B