Consider the following problem: The total number of pictures Bulan has uploaded to a website is increasing at a rate of r(t)=10-t pictures per week (where t is the time in weeks). At time t=2 weeks, Bulan had uploaded 30 pictures. How many pictures did Bulan upload between weeks 2 and 7 ? Which expression can we use to solve the problem? Choose 1 answer: (A) int_(2)^(7)r(t)dt (B) r(7) (C) int_(0)^(7)r(t)dt (D) r(7)-r(2)

Question

Consider the following problem: The total number of pictures Bulan has uploaded to a website is increasing at a rate of  r(t)=10-t pictures per week (where  t is the time in weeks). At time  t=2 weeks, Bulan had uploaded 30 pictures. How many pictures did Bulan upload between weeks 2 and 7 ? Which expression can we use to solve the problem? Choose 1 answer: (A)  int_(2)^(7)r(t)dt (B)  r(7) (C)  int_(0)^(7)r(t)dt (D)  r(7)-r(2)

Bytelearn · Accepted Answer

Define Integration Interval: To find the total number of pictures uploaded between weeks 2 and 7, we need to integrate the rate of uploading pictures, r(t), from t=2 to t=7. This is because the integral of a rate function over an interval gives the total amount accumulated over that interval.Mathematical Representation: The correct expression to use for this problem is the integral of r(t) from t=2 to t=7, which is represented mathematically as ∫(from t=2 to t=7) r(t) dt. This will give us the total number of pictures uploaded between these two times.Match with Answer Choices: Looking at the answer choices, we can see that option (A) ∫(from t=2 to t=7) r(t) dt matches our requirement. This is the integral of the rate function from week 2 to week 7, which is what we need to calculate.Incorrect Option (B): Option (B) r(7) is incorrect because it only gives the rate at which pictures are uploaded in the 7th week, not the total number of pictures uploaded between weeks 2 and 7.Incorrect Option (C): Option (C) ∫(from t=0 to t=7) r(t) dt is incorrect because it calculates the total number of pictures uploaded from the start (week 0) to week 7, not from week 2 to week 7.Incorrect Option (D): Option (D) r(7) - r(2) is incorrect because it subtracts the rate of uploading pictures at week 7 from the rate at week 2, which does not give the total number of pictures uploaded between these weeks.

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