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 an additional $570 on her computer between years 1 and 5 . (B) Julia spent $570 on her computer in the fifth year. (C) Julia spent an average of $570 per year purchasing and maintaining her computer. (D) By the end of the fifth year, Julia had spent a total of $570 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 an additional  $570 on her computer between years 1 and 5 . (B) Julia spent  $570 on her computer in the fifth year. (C) Julia spent an average of  $570 per year purchasing and maintaining her computer. (D) By the end of the fifth year, Julia had spent a total of  $570 purchasing and maintaining her computer.

Bytelearn · Accepted Answer

Given Equation Interpretation: The given equation is 420 + ∫_(1)^(5)r(t)dt = 570. We need to interpret what this equation means in the context of Julia's computer costs.Initial Cost Calculation: The term 420 represents the total amount Julia had spent on her computer by the end of the first year.Additional Cost Calculation: The integral ∫_(1)^(5)r(t)dt represents the total additional cost incurred for purchasing and maintaining the computer from year 1 to year 5.Total Cost Calculation: Adding the integral to 420 gives us the total cost spent on the computer by the end of the fifth year.Comparison of Options: The right side of the equation, 570, represents the total cumulative cost of purchasing and maintaining the computer by the end of the fifth year.Comparing the options given, we can see that option (A) is incorrect because it suggests Julia spent an additional $570 between years 1 and 5, which is not what the integral represents.Option (B) is incorrect because it suggests that Julia spent $570 in the fifth year alone, which is not indicated by the equation.Option (C) is incorrect because it suggests an average yearly cost, which is not what the equation or the integral represents.Option (D) is correct because it states that by the end of the fifth year, Julia had spent a total of $570 purchasing and maintaining her computer, which matches the interpretation of the equation.

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