The amount of money in Jim's bank account changes at a rate of r(t) dollars per month (where t is time in months). What does int_(0)^(1)r(t)dt=-100 mean? Choose 1 answer: (A) The amount of money in Jim's account increases by $100 each month. B Over the first month, the amount of money in Jim's account decreased by $100. (C) After one month, the amount of money in Jim's account was -$100. (D) The amount of money in Jim's account decreases by $100 each month.

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The amount of money in Jim's bank account changes at a rate of  r(t) dollars per month (where  t is time in months). What does  int_(0)^(1)r(t)dt=-100 mean? Choose 1 answer: (A) The amount of money in Jim's account increases by  $100 each month. B Over the first month, the amount of money in Jim's account decreased by  $100. (C) After one month, the amount of money in Jim's account was  -$100. (D) The amount of money in Jim's account decreases by  $100 each month.

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Question Prompt: Question prompt: What does the integral from 0 to 1 of r(t) dt equal to -100 signify about the change in the amount of money in Jim's bank account?Rate of Change Function: The integral of a rate of change function, r(t), over an interval gives the net change in the quantity over that interval. In this case, the integral represents the net change in the amount of money in Jim's bank account over the first month.Interpretation: Since the integral from 0 to 1 of r(t) dt is equal to -100, this means that the net change in the amount of money over the first month is a decrease of $100.Conclusion: The correct interpretation of the integral result is that over the first month, the amount of money in Jim's account decreased by $100. This corresponds to option (B).

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