In a certain section of the country,the price of chicken is currently $3 per kilogram.It is estimated that x weeks from now,the price will be increasing at a rate of $3 \sqrt { x + 1 }$ cents per kilogram.How much will chicken cost 4 weeks from now?
A)$4.20 per kilogram
B)$3.20 per kilogram
C)$2.21 per kilogram
D)$0.21 per kilogram

Question

Quizplus · Accepted Answer

To find the cost 4 weeks from now, integrate the rate of increase $3 \sqrt{x + 1}$ from 0 to 4, which gives the total increase in cents. The integral is $ \int_{0}^{4} 3 \sqrt{x + 1} \, dx = 2[(x+1)^{3/2}]_{0}^{4} = 2[(5)^{3/2} - (1)^{3/2}] = 2(11.1803 - 1) = 20.3606$ cents. Convert to dollars: $0.2036. Add this to the initial price: $3 + $0.2036 = $3.2036, approximately $3.20.

In a Certain Section of the Country,the Price of Chicken 3x+13 \sqrt { x + 1 }3x+1​

In a Certain Section of the Country,the Price of Chicken $3 \sqrt { x + 1 }$