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The cumulative profit a business has earned is changing at a rate of r(t) dollars per day (where t is the time in days). In the first 30 days, the business earned a cumulative profit of $1700. What does 1700+int_(30)^(90)r(t)dt represent? Choose 1 answer: (A) The time it takes for the cumulative profit to increase another $1700 after the first 30 days B The cumulative profit the business has earned as of day 90 (C) The rate at which the cumulative profit was increasing when t=90. (D) The change in the cumulative profit between days 30 and 90

The cumulative profit a business has earned is changing at a rate of r(t) r(t) dollars per day (where t t is the time in days). In the first 3030 days, the business earned a cumulative profit of $1700 \$ 1700 .\newlineWhat does 1700+∫3090r(t)dt 1700+\int_{30}^{90} r(t) d t represent?\newlineChoose 11 answer:\newline(A) The time it takes for the cumulative profit to increase another $1700 \$ 1700 after the first 3030 days\newline(B) The cumulative profit the business has earned as of day 9090\newline(C) The rate at which the cumulative profit was increasing when t=90 t=90 .\newline(D) The change in the cumulative profit between days 3030 and 9090

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Q. The cumulative profit a business has earned is changing at a rate of r(t) r(t) dollars per day (where t t is the time in days). In the first 3030 days, the business earned a cumulative profit of $1700 \$ 1700 .\newlineWhat does 1700+∫3090r(t)dt 1700+\int_{30}^{90} r(t) d t represent?\newlineChoose 11 answer:\newline(A) The time it takes for the cumulative profit to increase another $1700 \$ 1700 after the first 3030 days\newline(B) The cumulative profit the business has earned as of day 9090\newline(C) The rate at which the cumulative profit was increasing when t=90 t=90 .\newline(D) The change in the cumulative profit between days 3030 and 9090
  1. Understand given information: Understand the given information. We are given the cumulative profit for the first 3030 days, which is $1700\$1700. The expression ∫3090r(t)dt\int_{30}^{90}r(t)dt represents the integral of the rate of change of profit from day 3030 to day 9090. The integral of a rate of change gives us the total change over the interval.
  2. Interpret the integral: Interpret the integral. The integral ∫3090r(t)dt\int_{30}^{90}r(t)dt calculates the total additional profit earned from day 3030 to day 9090. It is the area under the curve of the rate function r(t)r(t) from t=30t=30 to t=90t=90.
  3. Combine with initial profit: Combine the initial profit with the integral. Adding the initial profit of $1700\$1700 to the integral gives us the total cumulative profit by day 9090. The expression 1700+∫3090r(t)dt1700 + \int_{30}^{90}r(t)dt represents the sum of the initial profit and the additional profit earned between days 3030 and 9090.
  4. Match expression to answer: Match the expression to the correct answer. The expression does not represent the time it takes for the profit to increase (eliminating option A), nor does it represent the rate of increase at a specific time (eliminating option C). It also does not represent just the change in profit (eliminating option D). Therefore, the expression represents the cumulative profit the business has earned as of day 9090, which is option B.

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