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.\nplan a: raise the price by $0.10 each week until the price reaches $12.00.\nplan b: raise the price by 10 percent each week until the price reaches $12.00.\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.\nplan d: raise the price by $0.25 each week until the price reaches $12.00.\nwhich plan will result in the price of the feed reaching $12.00 fastest?\nplan a\nplan b\nplan c\nplan 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.\nplan a: raise the price by $0.10 each week until the price reaches $12.00.\nplan b: raise the price by 10 percent each week until the price reaches $12.00.\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.\nplan d: raise the price by $0.25 each week until the price reaches $12.00.\nwhich plan will result in the price of the feed reaching $12.00 fastest?\nplan a\nplan b\nplan c\nplan d

Answer

Explanation:

Step1: Calculate time for Plan A

The price needs to increase by (12 - 8=$4). Since it increases by ($0.10) per week, the number of weeks (n_A=\frac{12 - 8}{0.10}=\frac{4}{0.10}=40) weeks.

Step2: Calculate time for Plan B

Let the number of weeks be (n_B). The price after (n_B) weeks is (P = 8\times(1 + 0.1)^{n_B}). We want (8\times(1.1)^{n_B}=12), so ((1.1)^{n_B}=\frac{12}{8} = 1.5). Take the natural logarithm of both sides: (n_B\ln(1.1)=\ln(1.5)), (n_B=\frac{\ln(1.5)}{\ln(1.1)}\approx\frac{0.4055}{0.0953}\approx4.25) weeks.

Step3: Calculate time for Plan C

The price needs to increase by (12 - 8=$4) over 8 weeks. But we can also check the rate. The total increase is (4) over (8) weeks, but we are just told it reaches (12) in 8 weeks.

Step4: Calculate time for Plan D

The price needs to increase by (12 - 8 = 4). Since it increases by ($0.25) per week, the number of weeks (n_D=\frac{12 - 8}{0.25}=\frac{4}{0.25}=16) weeks.

Answer:

B. plan B