The cumulative cost of purchasing and maintaining Julia's computer is increasing at a rate of r(t) dollars per year (where t is the time in years). At t=1, Julia had spent a total of $420 on her computer. What does 420+int_(1)^(5)r(t)dt=570 mean? Choose 1 answer: (A) Julia spent $570 on her computer in the fifth year. (B) By the end of the fifth year, Julia had spent a total of $570 purchasing and maintaining her computer. (C) Julia spent an additional $570 on her computer between years 1 and 5 . (D) Julia spent an average of $570 per year purchasing and maintaining her computer.

Question

The cumulative cost of purchasing and maintaining Julia's computer is increasing at a rate of  r(t) dollars per year (where  t is the time in years). At  t=1, Julia had spent a total of  $420 on her computer. What does  420+int_(1)^(5)r(t)dt=570 mean? Choose 1 answer: (A) Julia spent  $570 on her computer in the fifth year. (B) By the end of the fifth year, Julia had spent a total of  $570 purchasing and maintaining her computer. (C) Julia spent an additional  $570 on her computer between years 1 and 5 . (D) Julia spent an average of  $570 per year purchasing and maintaining her computer.

Bytelearn · Accepted Answer

Given Equation Interpretation: We are given the equation 420 + ∫_(1)^(5)r(t)dt = 570. This equation includes an integral, which represents the total additional cost from time t=1 to t=5. The initial value 420 represents the total cost at t=1. The equation is setting the sum of the initial cost and the additional cost over the next four years equal to 570.Integral Meaning: To understand what the equation means, we need to interpret the integral. The integral ∫_(1)^(5)r(t)dt represents the total additional cost of purchasing and maintaining the computer from year 1 to year 5. It does not represent the cost in any single year, but the cumulative additional cost over those years.Total Cost Calculation: Adding the initial cost of $420 to the integral gives us the total cost by the end of year 5. Therefore, the equation 420 + ∫_(1)^(5)r(t)dt = 570 means that by the end of the fifth year, Julia had spent a total of $570 on her computer.Answer Choice Evaluation A: Now we can evaluate the answer choices given: (A) This choice suggests that Julia spent $570 in the fifth year alone, which is incorrect because the integral represents the cumulative additional cost from years 1 to 5, not the cost in the fifth year only.Answer Choice Evaluation B: (B) This choice is correct because it states that by the end of the fifth year, Julia had spent a total of $570 on her computer, which is exactly what the equation represents.Answer Choice Evaluation C: (C) This choice is incorrect because it suggests that Julia spent an additional $570 between years 1 and 5, but the total amount spent by the end of year 5 is $570, not the additional amount spent.Answer Choice Evaluation D: (D) This choice is incorrect because it suggests an average yearly cost, which cannot be determined from the given equation without additional information about the function r(t).

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