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_(0)^(7)r(t)dt (B) r(7)-r(2) (C) int_(2)^(7)r(t)dt (D) r(7)

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_(0)^(7)r(t)dt (B)  r(7)-r(2) (C)  int_(2)^(7)r(t)dt (D)  r(7)

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Integrate rate function: 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 integration will give us the total amount accumulated over the time interval.Rate function integration: The rate function given is r(t) = 10 - t. To find the total number of pictures uploaded between weeks 2 and 7, we need to integrate this function from t=2 to t=7.Use correct expression: The correct expression to use for this integration is ∫ from 2 to 7 of r(t) dt. This corresponds to option (C) int_(2)^(7)r(t)dt.Perform integration: Now we perform the integration. The integral of r(t) = 10 - t with respect to t from 2 to 7 is:  ∫ from 2 to 7 of (10 - t) dt = [10t - (t^2)/2] from 2 to 7.Evaluate antiderivative: We evaluate the antiderivative at the upper and lower limits of integration:  [10(7) - (7^2)/2] - [10(2) - (2^2)/2] = [70 - 49/2] - [20 - 2] = [70 - 24.5] - [20 - 1] = 45.5 - 19 = 26.5.Round to nearest whole number: Therefore, Bulan uploaded 26.5 pictures between weeks 2 and 7. However, since the number of pictures must be a whole number, we should round to the nearest whole number if necessary. In this context, it seems like we should have an integer value for the number of pictures. This suggests there might be a mistake in the calculation.

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