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?\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.\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?\no plan a\no plan b\no plan c\no plan d

Answer

Answer:

B. plan B

Explanation:

Step1: Calculate weeks for Plan A

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

Step2: Calculate weeks for Plan B

Let the number of weeks be $n$. The formula is $8\times(1 + 0.1)^n=12$. So, $(1.1)^n=\frac{12}{8}=1.5$. Taking the natural logarithm of both sides: $n\ln(1.1)=\ln(1.5)$. Then $n=\frac{\ln(1.5)}{\ln(1.1)}\approx4.93$ weeks.

Step3: Calculate weeks for Plan C

The price increases over 8 weeks from $8$ to $12$. But we want to know when it first reaches $12$. Since it reaches $12$ in the 8th week, it takes 8 weeks.

Step4: Calculate weeks for Plan D

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

Since $4.93<8<16<40$, Plan B reaches $12$ fastest.