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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 cumulative profit the business has earned as of day 90
(B) The change in the cumulative profit between days 30 and 90
(C) The rate at which the cumulative profit was increasing when 
t=90.
(D) The time it takes for the cumulative profit to increase another 
$1700 after the first 30 days

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 cumulative profit the business has earned as of day 9090\newline(B) The change in the cumulative profit between days 3030 and 9090\newline(C) The rate at which the cumulative profit was increasing when t=90 t=90 .\newline(D) The time it takes for the cumulative profit to increase another $1700 \$ 1700 after the first 3030 days

Full solution

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 cumulative profit the business has earned as of day 9090\newline(B) The change in the cumulative profit between days 3030 and 9090\newline(C) The rate at which the cumulative profit was increasing when t=90 t=90 .\newline(D) The time it takes for the cumulative profit to increase another $1700 \$ 1700 after the first 3030 days
  1. Initial Cumulative Profit Explanation: The given expression is 1700+3090r(t)dt1700 + \int_{30}^{90}r(t)dt. This represents the initial cumulative profit of $1700\$1700 earned in the first 3030 days plus the integral of the rate of change of profit from day 3030 to day 9090.
  2. Rate of Change Integral Definition: The integral of a rate of change r(t)r(t) in this case) over an interval gives the net change in the quantity over that interval. Therefore, 3090r(t)dt\int_{30}^{90}r(t)\,dt represents the change in cumulative profit from day 3030 to day 9090.
  3. Total Cumulative Profit Calculation: Adding the initial cumulative profit of $1700\$1700 to the change in cumulative profit from day 3030 to day 9090 gives us the total cumulative profit by day 9090. Therefore, the expression 1700+3090r(t)dt1700 + \int_{30}^{90}r(t)dt represents the cumulative profit the business has earned as of day 9090.

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